## 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

**Correct Answer : B**

**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

**Correct Answer : D**

**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

**Correct Answer : D**

**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

**Correct Answer : D**

**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

**Correct Answer : D**

**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

**Correct Answer : C**

**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

**Correct Answer : A**

**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

**Correct Answer : B**

**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

**Correct Answer : B**

**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

**Correct Answer : D**

**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

**Correct Answer : D**

**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**

**answered ?**

A: 212

B: 266

C: 272

D: 312

**Correct Answer : B**

**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

**Correct Answer : D**

**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

**Correct Answer : B**

**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!

**Correct Answer : D**

**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!

**Correct Answer : A**

**17. The value of 74P2 is**

A: 2775

B: 150

C: 5402

D: none of these

**Correct Answer : C**

**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

**Correct Answer : B**

**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

**Correct Answer : C**

**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

**Correct Answer : C**