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AMCAT Permutations and Combinations Questions And Answer

AMCAT Permutations and Combinations Questions And Answer

1. In how many different ways can the letters of the word ‘OPTICAL’ be arranged so that the vowels

always come together ?

A: 120

B: 720

C: 4320

D: 2160

2. 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: 2880

D: 50400

3. How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by

5 and none of the digits is repeated ?

A: 5

B: 10

C: 15

D: 20

4. A committee is to be formed comprising 7 members such that there is a simple majority of men

and at least 1 women. The shortlist consists of 9 men and 6 women. In how many ways can this be

done?

A: 3,724

B: 3,630

C: 4,914

D: 5,670

5. From a pack of 52 playing cards, 4 cards are removed at random. In how many ways can the 1st

place and 3rd place cards be drawn out such that both are black ?

A: 64,974

B: 62,252

C: 69,447

D: 1,592,500

6. In how many ways can the digits 2,3,5,7 and 9 be placed to form a three-digit number so that the

higher order digit is always greater than the lower order digits? (Assume digits are all different).

A: 8

B: 9

C: 10

D: 15

7. In how many ways can 4 ladies and 4 men form two mixed doubles teams for a tennis match?

A: 72

B: 108

C: 36

D: 84

8. In CAT entrance examination paper there are 3 sections, each containing 5 questions. A candidate

has to solve 5, choosing at least one from each section. The number of ways he can choose is

A: 2,500

B: 2,250

C: 2,750

D: 3,250

9. A boy has 4 different boxes and 5 different marbles. In how many ways can he place the marbles

in the boxes such that each box has at least one marble ?

A: 560

B: 240

C: 420

D: 36

10. A teacher was trying to form the groups of students in such a way that every group has equal

number of students and that number should be a prime number. She tried for first 5 prime numbers, but on each occasion exactly one student was left behind. If t

A: 0

B: 2

C: 3

D: 4

11. Ram buys 7 novels from a book fair. Shyam buys 8 novels from the fair, none of which is common

with those bought by Ram. They decide to exchange their books one for one. In how many ways can

they exchange their books for the first time ?

A: 7!x8!

B: 7×8!

C: 7!x8

D: 56

12. In an examination 10 questions are to be answered choosing at least 4 from each of part A and

part B. If there are 6 questions in part A and 7 in part B, in how many ways can 10 questions be

A: 212

B: 266

C: 272

D: 312

13. A box contains 20 tickets of identical appearance, the tickets being numbered 1, 2, 3, ….., 20. In

how many ways can 3 tickets be chosen such that the numbers on the drawn tickets are in arithmetic

progression ?

A: 18

B: 33

C: 56

D: 90

14. A company could advertise about its new product in 4 magazines, 3 newspapers and 2 television

channels. But in a later move it decided to give advertisements in only 2 of the magazines, one of the

newspapers and one the TV channels. In how many ways can

A: 30

B: 36

C: 44

D: None of these

15. In how many ways can the letters of the word ‘ERGONOMICS’ be rearranged such that the vowels

always appear together?

A: 6! /2!

B: 6!*4!

C: 7! /2!

D: (7! * 4!)/2!

16. How many different four letter words can be formed (the words need not be meaningful) using

the letters of the word PACIFIC such that the first letter is P and the last letter is F?

A: 8

B: 3

C: 6

D: 7!/5!

17. The value of 74P2 is

A: 2775

B: 150

C: 5402

D: none of these

18. In how many different ways can the letters of the word ‘ HARDWARE’ be arranged in such a way

that the vowels always come together.

A: 120

B: 1080

C: 1440

D: 4320

19. In how many ways a committee, consisting of 4 men and 10 women can be formed from 6 men

and 10 women?

A: 266

B: 50

C: 15

D: 8640

20. Out of 7 consonants and four vowels ,how many words of three consonants and 2 vowels can be

formed?

A: 210

B: 1050

C: 25200

D: 21400