# 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.

- 100+ Permutation and Combination Aptitude Questions and Answers
- 1000+ Permutation and Combination Aptitude Questions with Solutions
- 1000+ Permutation and combination Questions for Competitive Exams
- 1000+ Tricky Maths Questions and Answers
- 1000+ Permutation and Combination Question Bank Pdf
- 1000+ Aptitude Questions and Answers 2023 - 2024
- 1000+ Permutation and Combination Questions for CAT
- 1000+ Permutations and Combinations Questions and Answers

Strength of Materials Questions and Answers Pdf More

Steam and Power Generation Quiz Questions & Answers Pdf More

Dc generator questions and answers pdf More

DC Generator Questions and Answers Pdf More

Electromagnetic Induction Quiz Questions and Answers More

Spring JBDC Interview Questions and Answers More

TNMAWS Mechanical Engineering Previous Year Question Papers Pdf More

History General Awareness Quiz Questions and Answers More

1000+ Sentence Rearrangement Questions for SSC CHSL Exam More

1000+ ICICI Bank Interview Questions and Answers Pdf More