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 = 8C4 = ($${8 × 7 × 6 × 5} / {4 × 3 × 2 × 1})$$ = 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 = 7C4 × 5C2 = 7C3 × 5C2 = $$({7 × 6 × 5} / {3 × 2 × 1}) × {5 × 4} / {2 × 1})$$ = 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 = (4C2 × 5C3) = (4C2 × 5C2)
= $$({4 × 3}/{2 × 1} × {5 × 4}/{2 × 1})$$ = 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 = (3C1 × 6C2) + (3C2 × 6C1) + (3C3)
= $$(3 × {6 × 5} / {2 × 1}) + ({3 × 2} / {2 × 1} × 6)$$ + 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 = (3C1 × 5C2) = $$3 × {5 × 4} / {2 × 1}$$ = 30.
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