100+ Permutation and Combination Aptitude Questions and Answers - 2

Question: 6

In how many ways can a cricket eleven be chosen out of 14 players?

(A) 200

(B) 300

(D) 382

View Answer

Ans: C

Required number of ways

= ¹⁴C₁₁ = ¹⁴C_(14-11) = ¹⁴C₃ = $${14 × 13 × 12} / {3 × 2 × 1}$$ = 364.

Question: 7

Out of 5 women and 4 men, a committee of three members is to be formed in such a way that at least one member is a woman. In how many different ways can it be done?

(A) 76

(B) 78

(D) 82

View Answer

Ans: C

Required number of ways = (⁵C₁ × ⁴C₂) + (⁵C₂ × ⁴C₁) + (⁵C₃)

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

= (30 + 40 + 10) = 80.

Question: 8

A committee of 5 members is to formed out of 3 trainees, 4 professors and 6 research associates. In how may different ways can this be done if the committee should have 2 trainees and 3 research associates?

(A) 20

(B) 40

(D) 80

View Answer

Ans: C

Required number of ways

= (³C₂ × ⁶C₃) = (³C₁ × ⁶C₃)

= $$(3 × {6 × 5 × 4} / {3 × 2 × 1})$$ = 60.

Question: 9

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

(A) 43

(B) 53

(D) 73

View Answer

Ans: C

Required no. of ways

= (⁷C₅ × ³C₂) = (⁷C₂ × ³C₁) =$${7 × 6} / {2 × 1} × 3$$ = 63.

Question: 10

A committee of 5 members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways can this be done, if the committee should have 4 professors and 1 research associate or all 3 trainees and 2 professors?

(A) 12

(B) 13

(D) 16

View Answer

Ans: C

Required number of ways = (⁴C₄ × ⁶C₁) + (³C₃ × ⁴C₂)

= (1 + 6) + $$(1 + {4 × 3} / {2})$$ = (7 + 7) = 14.

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100+ Permutation and Combination Aptitude Questions and Answers - 2

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