It is given that 2 particular players are never selected.

So total ways = 24*120 = 2880

So we will do selection from rest of the players which Another way approach: 4!*5! = 24*120 = 2880
means we will select 11 players out of 13 players. Type 11:
So total ways of selection = (15-2)C11 = 13C11 = There are 7 employees for 4 different posts. In how
(13*12)/(1*2) = 78 many ways we can fill the posts?
Type 9: Explanation:
A bowler and a wicket-keeper are to be chosen out First of all, we will select 4 employees out of total 7
of a team having 11 players. In how many different employees. The ways of selection are, 7C4 = 7C3 =
ways we can do this? (7*6*5)/(1*2*3) = 35
Explanation: After doing selection, we can arrange 4 employees for
First of all, we will select 2 players from total 11 4 different posts in 4! ways = 24 ways.
players. The ways of selection are 11C 2 = So total possible number of ways to fill the posts =
(11*10)/(1*2) = 55. After doing selection, we can 35*24 = 840
arrange 2 players on 2 different positions in 2! = 2 Another way approach: 7P4 = (7*6*5*4) = 840
ways. So total ways of selecting a bowler and a wicket- Type 12:
keeper = 11C2 *2! = 55*2 = 110 20 students are participating in a quiz. In how
Another way approach: 11P2 = 110 many ways can the first three prizes be won?
Type 10: Explanation:
In how many ways can the letters of the word First of all, we will select 3 students from total 20
SEQUOIAG be arranged so that all the vowels students. The ways of selection are, 20C3 =
come together? (20*19*18)/(1*2*3) = 1140
Explanation: After doing selection, we can arrange 3 students on 3
In word ‘SEQUOIAG’, we have 5 vowels positions in 3! = 6 ways.
(E,U,A,I,O) and 3 consonants (S,Q,G). According to So total possible number of ways in which the first
question, all five vowels should come together so we three prizes can be won = 1140*6 = 6840.
will assume these 5 vowels to take one place and other Another way approach: 20P3 = (20*19*18) = 6840
3 consonants will be arranged on 3 places, so total 4 ways
places. These practice sums cover the basics of
So ways to arrange these on 4 places will be 4! = 24 Probability & Permutations and Combinations
One important thing is that we can arrange the vowels and provide an opportunity to apply the concepts
order as well and we can do that in 5!= 120 ways. in different scenarios.

Practice Questions
1) In how many different ways can the letters of the a) 24 b) 60 c) 80 d) 110 e) 120 m
word “salty” be arranged?
2) Two unbiased coins are tossed. What is the d) 1/16 e) None of these
probability of getting exactly two heads?
a) ½ b) 1/3 c) ¼ d) ¾ e) None of these 14) One card is drawn at random from the cards.
What is the probability, if the card is neither jack
3) In how many ways the letters of the word nor queen?
“COURSE” can be arranged? a) 11/13 b) 9/13 c) 12/13
a) 360 b) 240 c) 540 d) 128 e) None of these d) 10/13 e) None of these

4) A dice is rolled, what is the probability of the 15) In how many ways the word “DETAILS” be
outcome being a prime number? arranged in that all vowels and consonants come
a) ½ b) 2/3 c) 5/6 d) 1/3 e) None of these together?
a) 144 b) 196 c) 72
5) In how many ways the letters of word d) 288 e) None of these
“SIMPLE” can be arranged so that all vowels come
together? 16) Two dice are rolled, find the probability that
a) 180 b) 210 c) 240 d) 270 e) 120 the sum is more than 10?
a) 5/18 b) 1/15 c) 1/12
6) If the bag contains 3 apples and 4 oranges, what d) 1/9 e) None of these
is the probability of choosing two oranges?
a) 1/7 b) 2/7 c) 3/7 d) 4/7 e) None of these 17) In how many ways the letters of the word
‘ARMOUR’ can be arranged?
7) Two students are selected from 8 students. How a) 720 b) 360 c) 120
many ways are there to achieve this? d) 650 e) None of These
a) 28 b) 64 c) 28 d) 52 e) None of these
18) Three letters are chosen out of the alphabets of
8) In a group of 5 red and 3 pink balls. In how many the English language. Find the probability that the
ways 2 red balls and one pink ball is selected? three letters are vowels.
a) 40 b) 50 c) 60 d) 30 e) 80 a) 1/230 b) 1/260 c) 2/65
d) 3/65 e) 3/260
9) If the box contains 4 red balls and 3 green balls,
what is the probability of picking two balls for same 19) A bag contains 4 red balls and three green balls.
color? If two balls are selected, in how many different
a) 2/5 b) 3/7 c) 4/9 d) 1/5 e) None of these ways the balls selected such that at least one red
ball should be there?
10) How many ways the letters of the word a) 18 b) 20 c) 36 d) 40 e) None of these
“CURRENT” be arranged?
a) 2520 b) 1260 c) 5040 d) 720 e) None of these 20) There is a group of 4 doctors and 6 teachers. If
4 persons are to be selected, in how many different
11) Two cards are drawn at random from a pack of ways can they be selected such that at least one
cards. What is the probability that both are Kings? teacher should be there?
a) 3/221 b) 4/221 c) 5/221 a) 211 b) 210 c) 209 d) 208 e) None of these
d) 1/221 e) None of these
21) A basket contains x apple, 4 oranges and 3
12) A bag contains 5 red balls and 7 blue balls. Find bananas. One fruit is taken out at random and the
the probability to choose 2 balls in same color. probability of getting an orange is 2/5 and find the
a) 1/66 b) 31/66 c) 29/66 value of x?
d) 1/22 e) 1/33 a) 2 b) 3 c) 1 d) 4 e) None of these

13) If the coin is tossed 5 times then what is the 22) In how many ways the word “MAGIC” can be
probability of getting two tails? arranged in such a way that all the consonants and
a) ¼ b) 5/16 c) 3/8 vowels always come together?
a) 24 b) 12 c) 48 d) 36 e) None of these
31) A box contains 8 Oranges and 15 Mangoes. Out
23) There are 5 black pencils, 3 white pencils and 2 of which 5 mangoes and 3 oranges are damaged. If
red pencils. If 2 pencils are selected at random, 2 fruits are drawn randomly, then what is the
what is the probability that none of them are black probability that both the fruits are non damaged
pencils? mangoes?
a) 2/3 b) 4/3 c) 2/5 d) 2/9 e) None of these a) 15/253 b) 45/253 c) 24/253
d) 11/253 e) None of these
24) If two dice are tossed, then what is the
probability of getting a sum is divisible by 5 32) A box contains 20 apples and 15 oranges. 40%
exactly? of the apples are rotten and 20% of the oranges are
a) 1/6 b) 1/36 c) 1/12 d) 1/9 e) None of these rotten. If three fruits are picked from the box at
random, find the probability that it does not
25) A bag contains 50 balls out of which 14 are red contain any rotten fruits.
balls, some are yellow balls and the remaining balls a) 184/595 b) 191/580 c) 141/581
are blue. If three balls are drawn from the bag, then d) 165/534 e) None of these
find the probability that balls are not red balls?
a) 59/190 b) 83/210 c) 23/170 33) In how many different ways a group of 5 men
d) 51/140 e) None of these and 7 women can be formed out of 8 men and 10
women?
26) Two dice are thrown simultaneously. What is a) 4240 b) 6380 c) 6720
the probability of getting a sum that is the perfect d) 5860 e) None of these
square?
a) 1/6 b) 1/3 c) 7/36 d) 4/9 e) 5/18 34) A box contains 4 red balls, 6 green balls and 2
blue balls. If two balls are drawn at random from
27) A box contains 4 white balls, 6 green balls and the box, then find the probability of that balls are
8 black balls. If four balls are picked at random, same colour?
find the probability that it contains at most 2 white a) 3/10 b) 7/12 c) 2/5
balls and at least 1 black ball and exactly 1 green d) 1/3 e) None of these
ball.
a) 300/700 b) 350/729 c) 525/343 35) A box contains x green balls, 4 pink balls and 5
d) 296/765 e) None of these red balls. If the probability of one red ball being
taken at random is 1/4, then find the total number
28) In how many different ways can the letters of of balls in the box?
the word “ESTABLISH” be arranged, so that all a) 20 b) 16 c) 24 d) 12 e) 18
vowels always come together? 36) How many words of 4 letters with or without
a) 7860 b) 8540 c) 15120 meaning are made from the letters of the word
d) 12380 e) None of these “MIXTURE” without repetition of letters?
a) 504 b) 840 c) 210
29) A bag contains 6 black balls, 3 green balls and d) 2520 e) None of these
x red balls and the probability of drawing a red ball
is 1/2, If a ball is drawn at random from the bag, 37) A box contains 4 red, 2 green and x yellow balls.
then find the probability that the ball is either black If two balls are drawn at random, then the
or green ball? probability of getting exactly one red and one
a) 1/9 b) 5/7 c) 3/10 d) 2/9 e) None of these yellow from the box is 16/45. Find the value of x?(x
value will be whole number)
30) Two cards are drawn at random from a pack of a) 3 b) 5 c) 6 d) 4 e) 2
52 cards. What is the probability that both the
cards are either Ace or Jack? 38) In a bag, the ratio of the number of red and
a) 5/221 b) 4/221 c) 1/221 black balls is 3:4 and the number of white balls in
d) 3/221 e) 2/221 the bag is 6. If one ball is drawn at random, then
the probability of that ball being black is 2/5. Find 46) In a class, there are 10 boys and 8 girls. 5
the number of red balls in the bag? students are selected randomly, Find the
a) 6 b) 9 c) 3 d) 12 e) None of these probability of getting 3 boys and 2 girls got
selected?
39) A bag contains 20 balls in which 5 yellow balls, a) 20/51 b) 20/73 c) 29/71
10 green balls and 5 white balls. If one ball is taken d) 27/107 e) None of these
at random, then find the probability of that ball
being yellow or green colour. 47) A bag contains 5 red balls, 2 blue balls and some
a) ½ b) 1/3 c) ¾ d) ¼ e) None of these black balls. If the probability of not getting a black
ball, when one ball picked randomly from the bag
40) In a group of 7 boys and 9 girls, 5 members are is 7/11, then find the number of black balls in the
to be selected. In how many different ways can they bag?
be selected such that at least one boy should be a) 5 b) 4 c) 2 d) 3 e) None of these
there?
a) 2450 b) 4242 c) 1840 48) A box contains x red balls, 4 yellow balls and 5
d) 4280 e) None of these blue balls. If the probability of one blue ball is
taken at random being 1/3, then what is the
41) A box contains 4 red balls, 5 white balls and 6 probability that two red balls is taken from the box
black balls. In how many different ways can 5 balls at random?
be selected from the box, if at least two red balls are a) 1/5 b) 1/6 c) 1/7 d) 1/3 e) 1/8
to be selected?
a) 1110 b) 1221 c) 1005 49) A box contains a certain number of apples,
d) 1250 e) None of these oranges and mangoes and the ratio of the number
of apples to oranges is 5:4 and the number of apples
42) Venkat has 14 fruits out of which 8 are fresh is equal to 150% of the number of mangoes. Find
fruits. In how many ways he can choose 6 fruits the probability of selecting three apples, if the sum
such that at least 4 of them are fresh fruits? of the total number of fruits in the box is 37?
a) 1550 b) 1244 c) 1414 a) 17/259 b) 30/407 c) 13/222
d) 1187 e) None of these d) 21/185 e) None of these

43) A box contains x red balls, (x + 3) green balls 50) A bag contains 24 balls of three different
and 3 pink balls. If one ball is drawn at random colours pink, yellow and blue respectively. The
from the box and then the probability of that ball number of yellow balls is 2 more than that of pink
being red is 1/3. If two balls are drawn at random, balls and the number of blue balls is 2 more than
then what is the probability that both the balls are that of yellow balls. If three balls are drawn at
pink? random, then find the probability that it contains 2
a) 1/51 b) 2/51 c) 1/17 pink and 1 blue ball.
d) 4/51 e) None of these a) 75/1012 b) 68/1512 c) 42/1813
d) 71/1000 e) None of these
44) A box contains 2 apples, x oranges and 6
bananas. If two fruits are drawn at random from 51) A box contains 4 blue balls, 5 pink balls and y
the box, then the probability that both the fruits are green balls and the probability of getting a green
apple is 1/66. Find the value of x? ball is 1/4. If two balls are drawn at random from
a) 3 b) 4 c) 5 d) 1 e) 2 the box, then find the probability that all the balls
are in same colour?
45) A bag contains 5 red balls, x black balls, (x + 3) a) 19/66 b) 5/72 c) 21/92
white balls and 3 green balls. If one ball is drawn at d) 7/51 e) None of these
random from the bag, then the probability of that
ball being white is 1/3. Find the value of x? 52) A box contains (x+2) yellow balls, 7 orange balls
a) 3 b) 2 c) 5 d) 1 e) 4 and x blue balls and the probability of selecting a
blue ball is 1/5. If three balls are drawn at random
from the box, then find the probability that all the 60) A bag contains x yellow balls and (x+5) green
balls are in different colour? balls. If the difference between the probability of
a) 5/19 b) 2/21 c) 1/9 getting a green ball and the probability of getting a
d) 3/13 e) None of these yellow ball is 1/3, then find the probability of
selecting two green balls from the bag?
53) In how many different ways can the letters of a) 4/7 b) 5/7 c) 2/7 d) 3/7 e) None of these
the word 'REASON' be arranged in such a way
that the vowels occupy only the odd positions? 61) A bag contains 24 balls of three different
a) 6 b) 36 c) 4 d) 16 e) None of these colours namely blue, pink and yellow the number
of blue balls in the bag are 8 and the number of
54) An Ice Hockey team of six players is to be pink balls is 4 more than the number of yellow
selected from a group of 8 male players and 4 balls. If two balls are picked from the bag, find the
female players. In how many ways a team is probability of selecting the same colour balls.
selected, having at least three female players? a) 6/7 b) 9/25 c) 8/21
a) 210 b) 224 c) 252 d) 260 e) 274 d) 22/69 e) None of these

55) A box contains 8 Black, 4 blue and (x + 1) Red 62) A box contains 7 red balls, 11 green balls and
balls. If two balls are taken out at random, then the some orange balls. The probability of selecting an
probability that the balls being red are 5/51. Find orange ball is 1/3. If three balls are drawn at
the number of Red balls in the box? random from the box, then find the probability that
a) 8 b) 7 c) 6 d) 10 e) None of these balls are red in colour?
a) 17/312 b) 11/270 c) 20/351
56)There are 3 wicket-keepers, 2 batters, 3 bowlers d) 7/585 e) None of these
and 1 all-rounder in a team, A captain can be
selected from these players. Find the probability 63) A box contains 12 oranges, 8 apples and a
that the selected captain is a wicket-keeper. certain number of bananas and the average
a) 1/3 b) 2/3 c) 4/5 d) 7/8 e) None of these number of fruits in the box are 9. 3 fruits are drawn
at random, then find the probability that at least 1
57) A box contains 12 handbags, x school bags and orange and at least 1 banana is drawn.
(x+2) travel bags. The probability of drawing a a) 61/30 b) 158/325 c) 155/321
handbag is 2/5. If four bags are drawn at random d) 154/325 e) None of these
from the box, then find the probability of selecting
2 school bags and 2 travel bags. 64) There are X corn flour and 9 besan flour
a) 4/87 b) 25/348 c) 11/203 packets in a box. If the probability of selecting one
d) 13/145 e) None of these corn packet from the box is 5/8, then find the
probability of selecting 1 corn flour and 2 besan
58) A box contains 3 Black pens, 5 Blue pens and 4 flour packets?
Red pens. 4 pens are drawn randomly, then what is a) 135/506 b) 131/506 c) 137/506
the probability that the pens contain at least 2 black d) 139/506 e) None of these
pens?
a) 23/55 b) 13/55 c) 27/55 65) A box contains x red, 5 pink and 6 black balls.
d) 39/55 e) None of these If one ball is drawn at random from the box and
the probability of that ball being pink is 1/3. If two
59) A box contains 45 balls of yellow, orange and balls are drawn at random from the box, then what
white balls. Ratio of the number of yellow to orange is the probability that at least one of them is black?
balls in the box is 4:5 and the ratio of the number a) 3/5 b) 2/25 c) 4/7 d) 5/7 e) None of these
of white to orange balls in the box is 6:5. If two balls
are drawn at random from the box, then find the 66) A bag contains x blue, 4 violet and 5 yellow
probability that at least one of the balls is orange? balls. One ball is taken out randomly from the bag,
a) 2/9 b) 1/3 c) 7/12 d) 5/11 e) None of these then the probability of getting a violet colour ball is
1/4. Find the total number of balls in the bag?
a) 14 balls b) 16 balls c) 10 balls
d) 12 balls e) None of these 73) In a group of 7 boys and 9 girls, 6 members are
to be selected. In how many different ways can they
67) In a bag, there are total 40 balls of red, blue and be selected such that at least one girl should be
pink. The number of blue balls in the bag is double there?
the number of red balls in the same bag and the a) 1378 b) 1024 c) 1452
number of pink balls in the bag is 5 more than that d) 1286 e) None of these
of blue balls. If two balls are drawn at random from
the bag, then find the probability that balls are 74) A bag contains X black balls, seven yellow balls,
blue? and eight red balls. If the probability of picking one
a) 16/39 b) 11/52 c) 7/60 black ball and one red ball is 32/117 when two balls
d) 13/97 e) None of these are randomly selected from the bag, find the
probability of randomly selecting 2 black balls
68) A box contains three different colours of from the bag.
balloons blue, black and red respectively and the a) 22/117 b) 23/117 c) 19/117
ratio of the number of blue, black and red balloons d) 17/117 e) None of these
is 5:3:6 and the difference between the number of
black and red balloons is 3. If 3 balloons are drawn 75) A box contains 12 red colour caps and some
at random from the box, find the probability that it white colour caps. If the probability of drawing a
contains at most 2 blue balloons. white cap from the box is 5/3 times of the
a) 161/191 b) 145/198 c) 51/8 probability of drawing a red colour cap from the
d) 177/182 e) None of these box. Then find the number of white colour caps in
the box?
69) A bag contains x red balls and y blue balls and a) 15 b) 23 c) 17 d) 20 e) None of these
the probability of selecting 1 red ball is 3/7 and the
probability of selecting 1 blue ball is 4/7. Find the 76) In how many ways word can the letters of the
ratio of the number of blue to red balls in the bag. word ‘NINTENDO’ be arranged in such a way that
a) 3:2 b) 3:4 c) 5:6 d) 4:3 e) None of these all the vowels come together?
a) 484 b) 720 c) 512 d) 676 e) None of these
70) A bucket contains 9 blue balls, x green balls and
y black balls. Two balls are drawn at random from 77) A bag contains 5 red, 2 black and 4 green balls
the bucket, then find the probability of that balls and another bag contains 3 red, 2 black and 5 green
are blue, if the probability of selecting a green ball balls. One ball is picked up from the 1st bag and
is 5/12 and the probability of selecting a black ball put in the second bag. Find the probability of
is 1/3. picking up green balls from the second bag now.
a) 5/36 b) 1/12 c) 7/24 d) 2/35 e) None of these a) 59/121 b) 57/121 c) 43/121
d) 61/121 e) None of these
71) There are 10 questions out of which 7 are to be
attended with a condition that minimum 4 78) If a basket contains 36 flowers and some of the
questions have to be attended from first 6 flowers are Yellow & others are Red. If a flower is
questions. How many ways can the questions be drawn at random from the basket, the probability
attended? of one flower being Red is 2/3. If three flowers are
a) 19 b) 60 c) 384 d) 8640 e) 75 picked at random, what is the probability of at least
one flower is Yellow?
72) A hat man has two bags. The big bag has 5 a) 123/138 b) 134/1323 c) 1279 / 1785
brown hats and 10 black hats, while the small bag d) 1212/1321 e) None of these
has 4 brown hats and 6 black hats. One hat is taken
out from any of these two bags. What is the 79) A bag contains x blue balls and 18 balls that are
probability that the hat taken out is black? both red and green together. The ratio of the
a) 19/30 b) 12/55 c) 13/60 number of red to green balls in the bag is 4:5. If the
d) 17/30 e) None of these probability of picking one red ball in the bag is 1/3,
then find the probability of picking two blue balls 86) A bag contains three colour balls i.e. black,
in the bag. white and red. The number of black balls is 5 less
a) 5/92 b) 3/92 c) 4/99 d) 2/99 e) 1/92 than that of red balls which is 3 less than that of
white balls. Find the total number of balls in the
80) In a bag there are ten balls, out these some red, bag if the probability of getting two red balls is 1/8.
some blue balls, and some black balls. The a) 11 b) 16 c) 19 d) 22 e) 13
probability of getting 2 red balls when 2 balls are
picked up randomly is 2/15. The ratio of the blue 87) A bag contains black balls, red balls, and yellow
and black ball is 2:1. If three balls are picked up balls. The ratio of number of black balls to red balls
from the bag without replacement, then find the is 4: 3 and yellow balls are 2 less than black balls.
probability of getting first red, second blue and If probability of picking out 1 black ball is 2/5, then
third black ball. find the probability of picking out 2 black balls?
a) 0.25 b) 0.044 c) 0.526 a) 16/95 b) 14/95
d) 0.355 e) None of these c) 14/75 d) None of these
e) 16/75
81) A person rolled dies four times. In how many
outcomes do we have two throws have the same 88) In a bag there are (a + 3) red balls, (b + 2) white
number and the other two something different? balls, and (3a + 5) yellow balls. The ratio of the
a) 360 b) 120 c) 480 d) 720 e) None of these number of red balls and white balls is 2:3
respectively and the number of yellow balls is
82) A bag contains some pens, pencils and erasers. 66.66% more than white balls. Find the probability
The number of Pens in bag is 8 and probability of of picking two red balls from a bag at random?
picking an eraser from bag is 1/10 less than that of a) 11/195 b) 9/195 c) 7/195
pencil. If the ratio of total items in bag to that of d) 19/195 e) None of these
pens is 5:2 respectively, then find the number of
pencils in that bag? 89) A bag contains red balls, white balls and black
a) 7 b) 5 c) 4 d) 6 e) None of these balls. The probability of picking two white balls
from bag is 21/190, and the probability of picking a
83) A bag contains certain number of fruits of three ball from bag such that ball is not red is 3/5. The
different varieties- apple, orange and banana. The number of red balls in bag (3Z – 4), and black balls
sum of the apple and orange is 13 which is 5 more in bag are Y, find difference between Z and Y?
than the number of apples in the bag. If two fruits a) 3 b) 1 c) 2
are drawn at random without replacement, then d) 4 e) Can’t be determined
the probability that first fruit is apple and the
second is banana is 14/95. Find the total number of 90) There are three boxes A, B and C and every box
fruits in the bag? has some apple and orange. Probability of one
a) 15 b) 18 c) 20 d) 22 e) 24 orange randomly selected from box A, box B and
box C is 1/3, 1/3 and 2/3 respectively. If the ratio of
84) When 2 students are selected from a group of x the total number of fruits in box A, B and C is 4:3:5
boys and 7 girls, the probability of same gender is and all the three box’s fruits are mixed in box D,
31/66. What is the probability that when 3 people then what is the probability of one orange is drawn
are selected at random, all 3 are boys? (x should be at random from box D?
whole number) a) 11/32 b) 1/6 c) 3/8
a) 1/22 b) 3/22 c) 5/21 d) 4/21 e) 2/11 d) 17/36 e) 5/12

85) A series of 7 matches is played between teams 91) There are three types of swans (black, whooper
A and B and no match ended in a draw. In how and mute) swimming in a lake. The number of
many number of ways the series can be won by black swans swimming in a lake is (x+5) and the
team A? average number of whooper and mute swans
a) 56 b) 48 c) 72 d) 64 e) 80 swimming in a lake is 37.5. If two swans started to
fly and the probability that both swans being black
is 2/33, then find the total number of swans each category. Then find the probability that he
swimming in a lake? performs with only white colour?
a) 150 b) 90 c) 120 d) 100 e) None of these a) 22/225 b) 8/225 c) 4/225
d) 23/125 e) None of these
92) A bag contains 5 red balls, x blue balls and 7
black balls and the probability of selecting 1 blue 97) A bag contains three different colour balls they
ball is 1/4. If three balls are drawn at random, find are Blue, Pink, and orange. The total number of
the probability that it contains at least 1 red ball orange and pink colour balls in the bag is 22. The
and at least 1 blue ball. probability of picking a blue colour ball from the
a) 2/3 b) 1/8 c) 5/7 d) 3/8 e) None of these bag is 6/17. If the sum of blue and orange colour
balls in the bag is 22, then find the probability of
93) In a running race competition involving some picking two pink colour balls from the bag.
boys and girls of an apartment, every member had a) 2/17 b) 4/17 c) 5/17
to play exactly one race with every other member. d) 7/34 e) None of these
It was found that in 10 races both the players were
boys and in 45 races both the members were girls. 98) A bag contains Z red balls, 2Y black balls and
Find the number of races in which one member was Y white balls. The Probability of picking three balls
a boy and other was a girl. from bag at random, such that all are of different
a) 50 b) 40 c) 30 d) 20 e) None of these colour is 9/40. Find the value of (2Z + 3Y) if the
total number of balls in the bag is 16
94) How many 5 letter words starting with the a) 20 b) 19 c) 21 d) 28 e) None of these
vowel can be formed by the letter of the word
‘STREAMFLOW’ such that no letter in the word 99) In a store, three types of items-pants, shirts and
is getting repeated? bags are sold. Pants sold are 50% of the shirts sold.
a) 5822 b) 9260 c) 4526 Find the average of total items sold if the
d) 7284 e) None of these probability of drawing a bag is1/3when an item is
drawn randomly from the total sold items and
95) A box contains certain number of bulbs out of number of bags sold are 8 less than that of shirts
which 40% bulbs are red and rest are blue. Two sold?
bulbs are randomly drawn from the box, such that a) 24 b) 34 c) 14 d) 28 e) None of these
the probability that a red ball and a blue ball are
drawn is 32/65. Find the total number of balls in the 100) If Bag A contains 4 red balls and 6 white balls.
box. Bag B contains 4 red balls and 10 white balls. One
a) 25 b) 26 c) 39 d) 40 e) None of these ball is picked from bag A and mixed with balls in
bag B, then 2 balls are drawn from bag B. Find the
96) A box contains 15 caps, 15 marbles and 15 pens probability that both the balls are white?
of black, green and white colours in the ratio of a) 17/35 b) 11/35 c) 19/35
3:7:5,5:3:7 and 7:5:3 respectively. The person does d) 22/35 e) 18/35
his performance on the box by using one item of

Answer Key
1. E 11. D 21. B 31. B 41. B 51. A 61. D 71. B 81. D 91. D
2. C 12. B 22. A 32. A 42. C 52. D 62. D 72. A 82. A 92. D
3. E 13. B 23. D 33. C 43. A 53. B 63. D 73. E 83. C 93. A
4. A 14. A 24. E 34. D 44. B 54. C 64. A 74. A 84. A 94. E
5. C 15. D 25. D 35. A 45. B 55. C 65. E 75. D 85. D 95. D
6. B 16. C 26. C 36. B 46. A 56. A 66. B 76. B 86. B 96. E
7. C 17. B 27. E 37. D 47. B 57. A 67. C 77. A 87. B 97. A
8. D 18. B 28. C 38. A 48. C 58. B 68. D 78. C 88. C 98. E
9. B 19. A 29. E 39. C 49. C 59. E 69. D 79. A 89. B 99. A
10. A 20. C 30. E 40. B 50. A 60. D 70. D 80. B 90. D 100. A

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