SINGH COMMERCE ACADEMY
9th, 10th, 11th, 12th (Commerce+Maths)
B.Com, BBA, MBA Contact: 9993382868
PERMUTATIONS AND COMBINATIONS
1. Evaluate 4 !−3!
2. If C=na¿ nbC ¿ , find n.
3. Given 5 flags of different colours, how many different signals can be generated if each
signal requires the use of 2 flags one below the other.
4. How many 4 letter code can be formed using the first 10 letters of the English
alphabet, if no letter can be repeated?
8!
5. Compute 6 ! ×2 !
6. If C=n8¿ n2C ¿, find n2C .
7. In how many ways 9 balls can be selected from 6 red, 5 white and 5 blue balls, if each
selection consists of 3 balls of each colour.
8. Find r, if 5. P=4r ¿ 6. r−15 P ¿
9. How many words, with or without meaning each of 2 vowels and 3 consonants can be
framed from the letters of the word DAUGHTER?
10.Find n, if 2 n3C : n3C =11: 1
11.How many words, with or without meaning can be formed using all the letters of the
word EQUATION at a time so that vowels and consonants occur together.
12.How many words, with or without meaning can be formed from the letters of the word
MONDAY. Assuming that no letter is repeated, if
(a) 4 letters are used at a time.
(b) All letters are used but first letter is a vowel.
13.In how many ways 5 girls and 3 boys be seated in a row so that no two boys are
together?
14.Find the number of arrangements of the letters of the word INDEPENDENCE. In how
many of these arrangements
(a) Do the words start with P
(b) Do all the vowels always occur together
15.Find n, if n−13 P: n4 P=1 :9
16.In how many can we select a cricket team of eleven from 17 players in which only 5
players can bowl if each cricket team of 11 must include exactly 4 bowlers?
17.In how many ways can the letters of the word ASSASSINATION be arranged so that
all the S’s are together?
18.In how many ways can the letters of the word MISSISSIPPI be arranged so that all the
I’s do not come together?
19.Find the number of permutations of the letters of the word ALLAHABAD.
20.A group consists of 4 girls and 7 boys. In how many can a team of 5 members be
selected if the team has:
(a) No girl
(b) At least one boy and one girl
(c) At least 3 girls
21.If the letters of the word AGAIN are arranged as in dictionary, what will be the 50th
word?
22.What is the number of ways of selecting 4 cards from a pack of 52 playing cards? In
how many of these
(a) Four cards are of the same suit
(b) Four cards belong to 4 different suits
(c) Are face cards
(d) 2 are red cards and 2 are black cards
(e) Cards are of the same colour
23.In how many ways can the letters of the word PERMUTATIONS be arranged if the
(a) Words start with P and end with S
(b) Vowels are always together
(c) There are always 4 letters between P and S
