# 100+ Permutation and Combination Aptitude Questions and Answers - 1

Question: 1

In how many ways can a committee of 4 people be chosen out of 8 people?

(A) 32

(B) 52

(C) 70

(D) 79

Ans: C

Required number of ways =^{8}C

_{4}= ($${8 × 7 × 6 × 5} / {4 × 3 × 2 × 1})$$ = 70.

Question: 2

In how many ways, a committee of 6 members be selected from 7 men and 5 ladies, consisting of 4 men and 2 ladies?

(A) 250

(B) 350

(C) 450

(D) 550

Ans: B

We have to select (4 men out of 7) and (2 ladies out of 5).

∴ Required number of ways =
^{7}C_{4} × ^{5}C_{2} = ^{7}C_{3} × ^{5}C_{2} = $$({7 × 6 × 5} / {3 × 2 × 1}) × {5 × 4} / {2 × 1})$$ = 350.

Question: 3

A committee of 5 members is to be formed by selecting out 4 men and 5 women. In how many different ways the committee can be formed if it should have 2 men and 3 women?

(A) 30

(B) 60

(C) 70

(D) 80

Ans: B

Required number of ways = (^{4}C_{2} × ^{5}C_{3})
= (^{4}C_{2} × ^{5}C_{2})

= $$({4 × 3}/{2 × 1} × {5 × 4}/{2 × 1})$$ = 60.

Question: 4

A box contains 2 white, 3 black and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least 1 black ball is to be included in the draw?

(A) 32

(B) 48

(C) 64

(D) 72

Ans: C

We may have (1 black and 2 non black) or (2 black and 1 non black) or (3 black).

Required no. of .ways = (^{3}C_{1} × ^{6}C_{2}) + (^{3}C_{2} × ^{6}C_{1}) + (^{3}C_{3})

= $$(3 × {6 × 5} / {2 × 1}) + ({3 × 2} / {2 × 1} × 6)$$ + 1 = (45 + 18 + 1) = 64.

Question: 5

Out of 5 men and 3 women, a committee of three members is to be formed so that it has 1 woman and 2 men. In how many different ways can it be done?

(A) 10

(B) 20

(C) 30

(D) 40

Ans: C

Required number of ways = (^{3}C_{1} × ^{5}C_{2}) = $$3 × {5 × 4} / {2 × 1}$$ = 30.

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