Permutation & Combination Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions

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The following question based on Permutations & Combination topic of quantitative aptitude

Questions : A boy has 3 library cards and 8 books of his interest in the library. Of these 8, he does not want to borrow chemistry part II unless Chemistry part I is also borrowed. In how many ways can he choose the three books to be borrowed ?

(a) 26

(b) 27

(c) 41

(d) 56

e) None of these

The correct answers to the above question in:

Answer: (c)

Two possibilities are there :

(i) Chemistry part I is available in 8 books with Chemistry part II.

or

(ii) Chemistry part II is not available in 8 books but Chemistry part I is available.

Total No. of ways = 1× 1 ×$^6C_1 + ^7C_3$ = 6 + ${7 × 6 × 5}/{3 × 2}$ = 6 + 35 = 41

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Read more model questions set 1 Based Quantitative Aptitude Questions and Answers

Question : 1

In how many different ways can be letters of the word 'CYCLE' be arranged?

a) 30

b) 4240

c) 80

d) 120

e) None of these

Answer: (e)

CYCLE whereas C comes two times.

So, arrangements are = ${5!}/{2!}$ = ${5 × 4 × 3 × 2}/{2}$ = 60 ways

Question : 2

How many different ways can the letters in the word ATTEND be arranged?

a) 240

b) 120

c) 80

d) 60

e) None of these

Answer: (e)

There are 6 letter in the word 'ATTEND' whereas, T comes two times.

So, required number of ways = ${6!}/{2!}$ = ${720}/{2}$ = 360

Question : 3

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by :

a) 5! × 4!

b) 30

c) 7! × 5!

d) 6! × 5!

e) None of these

Answer: (d)

No. of ways in which 6 men and 5 women can dine at a round table = 6! × 5!

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Permutation & Combination Model Questions Set 1

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