PRACTICE QUESTIONS
ZIDD
PERMUTATION & COMBINATION
1. The number of ways the letters of the word MISSISIPPI can be arranged so that the three S’s are
inseparable.
(A) 840
(B) 720
(C) 1440
(D) 560
2. Using the digits 0, 2, 5, 6, 7 and 9 only once how many 4 digit even numbers can be formed?
(A) 180
(B) 144
(C) 156
(D) 96
3. 8 students are to be arranged in a line. The number of arrangements in which there will be 3
students between two particular students are
(A) 5040
(B) 5760
(C) 4320
(D) 3360
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4. 3 ladies and 5 gents are to be seated on a circular table, then the numbers ways in which exactly 2
out of 3 ladies will sit together is
(A) 3! 4!
(B) 6 5!
(C) 24 5!
(D) None of these
5. There are 3 Physics books, 3 Maths books and 2 Biology books, then number of ways in which there
is ateast one other subject books between any two Maths books is
(A) 6! 20
(B) 6! 56
(C) 5! 40
(D) None of these
6. The number of arrangements of the word “ASSOCIATION” so that vowels occupy odd places is
5! ×5!
(A) 2!3
5! ×5!
(B)
2!4
6! ×5!
(C)
2!3
(D) 5400
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7. A paper consists of 5 questions of Maths and 3 questions on Stats. In how many ways a student can
attempt the paper such that he attempts atleast one question from each.
(A) 255
(B) 217
(C) 5! 3!
(D) 15
8. The number of ways 10 persons can be divided into four groups containing 2, 2, 3 and 3 persons
(A) 25200
(B) 12600
(C) 6300
(D) None of these
9. If 10
C3 2. 10 C4 10C5 nC5 then value of n is:
(A) 10
(B) 11
(C) 12
(D) 13
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10. A polygon has 65 diagonals, then the number of lines that can be forms using the vertices of this
polygon is
(A) 65C2
(B) 13C2
(C) 65C2 - 65
(D) 13C2 – 13
11. The number of factors of the number 840 will be
(A) 32
(B) 31
(C) 30
(D) 29
12. A person has 3 library cards and 10 books of his choice (out of which two are Maths part 1 and part
2). In how many ways he can get 3 books issued such that the takes Maths part 2 only when when
takes Maths part 1.
(A) 10C3
(B) 9C3
(C) 84
(D) 92
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13. Number of Triangles and Lines that can be formed from 11 points in a plan out of which 5 are
collinear is
(A) 155, 45
(B) 165, 46
(C) 155 , 46
(D) 165, 45
14. The number of ways a committee of 6 members is can be selected from 6 ladies and 5 gents such that
gents are in majority is
(A) 81
(B) 281
(C) 136
(D) 75
15. Using the digits 1, 2, 0, 5, 9 only once how many odd number less than 10000 can be formed?
(A) 54
(B) 64
(C) 75
(D) 93
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16. The ratio n + 1Pr :nPr -1 is
(A) n - 1
(B) n + 1
(C) n
(D) n - 2
17. How many new words can be formed using the letter of ‘PATNA’?
(A) 60
(B) 120
(C) 59
(D) 119
18. If six persons are selected out of ten, in how many ways will a particular person be found among
those six?
(A) 84
(B) 126
(C) 192
(D) 144
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19. The number of triangles that can be formed with the 10 points as vertices, n of which are collinear is
110, then n is
(A) 3
(B) 4
(C) 5
(D) 6
20. (n + 2)! = 120(n – 1)!, then (n+ 4)! =
(A) 5040
(B) 40320
(C) 720
(D) 120
ANSWER KEY
1 A 2 C 3 B 4 C 5 D
6 D 7 B 8 C 9 C 10 B
11 B 12 D 13 C 14 A 15 D
16 B 17 C 18 B 19 C 20 A
Speed Test
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1. There are 20 points in a plane area. How many triangles can be formed by these points if
5 points are collinear?
(A) 550 (B) 560 (C) 1130 (D) 1140
2. If nPr =3024 and nCr =126, then find n and r
(A) 9, 4 (B) 10, 3 (C) 12, 4 (D) 11, 4
3. How many 3 digit odd numbers can be formed using the digits 5, 6, 7, 8, 9, if the digits
can be repeated?
(A) 55 (B) 75 (C) 65 (D) 85
4. In how many different ways can the letters of the word 'CORPORATION' be arranged so
that the vowels always come together?
(A) 810 (B) 1440 (C) 25200 (D) 50400
5. If 15C3r = 15Cr+3 then r is equal to
(A) 5 (B) 4 (C) 3 (D) 2
6. Find 'n' if nP₂=72
(A) 10 (B) 8 (C) 12 (D) 9
7. A committee of 3 women and 4 men is to be formed out of 8 women and 7 men. Mrs.
Kajal refuses to serve in a committee in which Mr. Yash is a member. The number of such
committees can be:
(A) 1530 (B) 1500 (C) 1520 (D) 1540
8. If 6 P2r 12 6Pr , then r is equal to
(A) 1 (B) 2 (C) 3 (D) 4
9. In how many different ways can the letters of the word ‘SOFTWARE’ be arranged so that
the vowels always come together?
(A) 720 (B) 1440 (C) 2880 (D) 4320
10. In the next world cup of cricket, there will be 12 teams divided equally into two equal
groups. Team of each group will play a match against other teams of the group. From
each group, 3 top teams will qualify for next round. In this round, each team will play
against each other. Four top teams of this round will qualify for semi- finals and play
against each other and then two top teams will go to final, where they play the best of
three matches. How much minimum number of matches in the next world cup will be?
(A) 54 (B) 53 (C) 38 (D) 43
11. A user wants to create a password using 4 lowercase letters (a – z) and 2 uppercase
letters (A-Z). No letter can be repeated in any form. In how many ways can the password
be created if the passward must start with an uppercase letter?
(A) 26 × 25 × 24 × 23 × 22 × 5 × 21
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(B) 26 × 25 × 24 × 23 × 22 × 2 × 21
(C) 26 × 5 × 25 × 24 × 23 × 2 × 22 × 21
(D) 6 × 26 × 25 × 24 × 23 × 22 × 21
12. In how many ways can 5 boys and 3 girls sit in a row so that no two girls are together
(A) 14,400 (B) 14,000 (C) 14,425 (D) 12,400
13. In how many ways the letters of the word “STADIUM” be arranged in such a way that the
vowels all occur together?
(A) 7!/3! (B) 5! 4! (C) 5! 3! (D) 7! 3!
14. How many ways can 5 different trophies can be arranged on a shelf if one paticular
trophy must always be in the middle?
(A) 24 (B) 120 (C) 48 (D) 144
15. In a party every person shakes hands with every other person. If there are 105
handshakes in total, find the number of persons in the party.
(A) 14 (B) 15 (C) 21 (D) 22
16. A selection is to be made for one post of Principal and two posts of Vice-Principal.
Amongst the six candidates called for the interview, only two are eligible for the post of
Principal, while they all six are eligible for the post of Vice-Principal. The number of
possible combinations for the selection is:
(A) 4 (B) 12 (C) 18 (D) 20
17. In a class of 4 boys and 3 girls, they are required to sit in a row in such a way that no two
girls can sit together. Compute, in how many different ways they can sit together.
(A) 60 (B) 480 (C) 720 (D) 1,440
18. How many total combinations can be formed of 8 different counters marked as 1, 2, 3, 4,
5, 6, 7 & 8, taking 4 counters at a time and there being at least one odd and one even
numbered counter in each combination?
(A) 68 (B) 66 (C) 64 (D) 62
Answer Key – Speed Test
1 C 2 A 3 B 4 D 5 C
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6 D 7 D 8 B 9 D 10 B
11 A 12 B 13 C 14 A 15 B
16 D 17 D 18 A
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