ABC26GN5309 · Permutations and Combinations

Subject: General Aptitude · Chapter: Permutations and Combinations · Exam: · Marks: · Difficulty:

From a group of 7 men and 6 women, 5 persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done? 845

(a)564

(b)645

(c)735

(d)756

(e)None of these

Answer

Answer (as printed): A

Explanation

Required number of ways = (7C3 × 6C2) + (7C4 × 6C1) + (7C5 × 6C0) 7 × 6 × 5 6 × 5  7 6 7 =  ×  + ( $\mathrm{C_{3}}$ × $\mathrm{C_{1}}$ ) + ( $\mathrm{C_{2}}$ × 1)  3 2   7 × 6 × 5 6 × 5  7 × 6 × 5  7 × 6  =  × + × 6 +  × 1  6 2 × 1   3 × 2 × 1  2×1  = (525 + 210 + 21) = 756.

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