# AMCAT Previous Years Questions on Permutations and Combinations

 Topics Sub- Topics Expected Ques Basic Mathematics 6 - 8 Questions Applied Mathematics 8 - 10 Questions Engineering Mathematics 8 - 10 Questions

Ques. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels

always come together ?

Op 1: 120

Op 2: 720

Op 3: 4320

Op 4: 2160

Op 5: None of these

Correct Op : 2

Ques. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the

vowels always come together ?

Op 1: 810

Op 2: 1440

Op 3: 2880

Op 4: 50400

Op 5: 5760

Correct Op : 4

Ques. 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 ?

Op 1: 5

Op 2: 10

Op 3: 15

Op 4: 20

Op 5:

Correct Op : 4

Ques. 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?

Op 1: 3,724

Op 2: 3,630

Op 3: 4,914

Op 4: 5,670

Op 5:

Correct Op : 3

Ques. 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 ?

Op 1: 64,974

Op 2: 62,252

Op 3: 69,447

Op 4: 1,592,500

Op 5:

Correct Op : 4

Ques. 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).

Op 1: 8

Op 2: 9

Op 3: 10

Op 4: 15

Op 5:

Correct Op : 3

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

Op 1: 72

Op 2: 108

Op 3: 36

Op 4: 84

Op 5:

Correct Op : 1

Ques. 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

Op 1: 2,500

Op 2: 2,250

Op 3: 2,750

Op 4: 3,250

Op 5:

Correct Op : 2

Ques. 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 ?

Op 1: 560

Op 2: 240

Op 3: 420

Op 4: 36

Op 5:

Correct Op : 2

Ques. 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

Op 1: 0

Op 2: 2

Op 3: 3

Op 4: 4

Op 5:

Correct Op : 4

Ques. 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 ?

Op 1: 7!x8!

Op 2: 7x8!

Op 3: 7!x8

Op 4: 56

Op 5:

Correct Op : 4

Ques. 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

Op 1: 212

Op 2: 266

Op 3: 272

Op 4: 312

Op 5:

Correct Op : 2

Ques. 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 ?

Op 1: 18

Op 2: 33

Op 3: 56

Op 4: 90

Op 5:

Correct Op : 4

Ques. 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

Op 1: 30

Op 2: 36

Op 3: 44

Op 4: None of these

Op 5:

Correct Op : 2

Ques. In how many ways can the letters of the word 'ERGONOMICS' be rearranged such that the vowels

always appear together?

Op 1: 6! /2!

Op 2: 6!*4!

Op 3: 7! /2!

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

Op 5:

Correct Op : 4

Ques. 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?

Op 1: 8

Op 2: 3

Op 3: 6

Op 4: 7!/5!

Op 5:

Correct Op : 1

Ques. The value of 74P2 is

Op 1: 2775

Op 2: 150

Op 3: 5402

Op 4: none of these

Op 5:

Correct Op : 3

Ques. In how many different ways can the letters of the word ' HARDWARE' be arranged in such a way

that the vowels always come together.

Op 1: 120

Op 2: 1080

Op 3: 1440

Op 4: 4320

Op 5: 720

Correct Op : 2

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

and 10 women?

Op 1: 266

Op 2: 50

Op 3: 15

Op 4: 8640

Op 5: none of these

Correct Op : 3

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

formed?

Op 1: 210

Op 2: 1050

Op 3: 25200

Op 4: 21400

Op 5: none of these

Correct Op : 3

Ques. 3 books of mathematics and 5 books of physics are placed on a shelf so that the books on the

same subject always remain together .The possible arrangements are .

Op 1: 1440

Op 2: 1956

Op 3: 720

Op 4: none of these

Op 5:

Correct Op : 1

Ques. The number of possible selections of one or more questions from 8 given questions, each

question having an alternative, is

Op 1: 28-1

Op 2: 38-1

Op 3: 48-1

Op 4: none of these

Op 5:

Correct Op : 2

Ques. A five -digit number divisible by 3 is to be formed using numerals 0,1,2,3,4 and 5 without

repetition. The total number of ways this can be done is

Op 1: 216

Op 2: 240

Op 3: 600

Op 4: 3125

Op 5:

Correct Op : 1

Ques. Let A be containing 10 distinct elements ,then the total number of distinct functions from A to A IS

Op 1: 10!

Op 2: 1010

Op 3: 210

Op 4: 210-1

Op 5:

Correct Op : 2

Ques. A polygon has 44 diagonals, the number of its sides is

Op 1: 10

Op 2: 11

Op 3: 12

Op 4: 22

Op 5:

Correct Op : 2

Ques. The number of triangles that can be formed by choosing the vertices from a set of 12 points,

seven of which lie on the same straight line is

Op 1: 105

Op 2: 115

Op 3: 175

Op 4: 185

Op 5:

Correct Op : 4

Ques. There are 5 letters and five addressed envelops. the number of ways in which all the letters can

be put in wrong envelops is

Op 1: 119

Op 2: 44

Op 3: 59

Op 4: 40

Op 5:

Correct Op : 2

Ques. The number of ways in which 8 different flowers can be strung to form a garland so that 4

particular flowers are never separated is

Op 1: 960

Op 2: 2880

Op 3: 288

Op 4: 576

Op 5:

Correct Op : 2

Ques. At an election there are five candidates and three members to be elected , and a voter may vote

for any number of candidates not greater than the number to be elected. Then the number of ways in

which a voter may vote is

Op 1: 25

Op 2: 30

Op 3: 32

Op 4: none of these

Op 5:

Correct Op : 4

Ques. There are n different books and p copies of each. the number of ways in which a selection can be

Op 1: np

Op 2: pn

Op 3: (p+1)n -1

Op 4: (n+1)p-1

Op 5:

Correct Op : 3

Ques. The sides AB, BC, CA of a triangle ABC have 3,4 and 5 interior points respectively on them. The

total number of triangles that can be constructed by using these points as vertices is

Op 1: 220

Op 2: 204

Op 3: 205

Op 4: 195

Op 5:

Correct Op : 3

Ques. A lady gives dinner party to five guests to be selected from 9 friends .The number of ways of

forming the party of 5,given that two of the friends will not attend the party together is

Op 1: 56

Op 2: 126

Op 3: 91

Op 4: none of these

Op 5:

Correct Op : 3

Ques. Each question has four choices out of which only one is correct. A candidate has to answer four

questions. The number of ways he fails to give all answers correctly, is

Op 1: 15

Op 2: 81

Op 3: 255

Op 4: 256

Op 5:

Correct Op : 3

Ques. A college has 10 basketball players. A 5-member team and a captain will be selected out of these

10 players. How many different selections can be made?

Op 1: 1260

Op 2: 210

Op 3: 10C6 * 6!

Op 4: 10C5 * 6

Op 5:

Correct Op : 1

Ques. There are 10 yes or no questions. How many ways can these be answered?

Op 1: 1084

Op 2: 2048

Op 3: 1024

Op 4: 100

Op 5:

Correct Op : 3

Ques. If the letters of the word CHASM are rearranged to form 5 letter words such that none of the

word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word

CHASM?

Op 1: 24

Op 2: 31

Op 3: 32

Op 4: 30

Op 5:

Correct Op : 3