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CA Foundation · Quantitative Aptitude · Permutations and Combinations

A committee of 5 is to be formed from 6 men and 4 women such that it contains at least 2 women. In how many ways can this be done?

The answer is 186. Counting directly: 2 women and 3 men give 120 ways, 3 women and 2 men give 60 ways, and 4 women and 1 man give 6 ways. Adding gives 186. Equivalently, 252 total selections minus 66 with fewer than two women.

  1. A186
  2. B246Correct
  3. C252
  4. D210

Explanation

Total ways = 10C5 = 252. Subtract the cases with fewer than 2 women: 0 women = 6C5 = 6; 1 woman = 4C1 × 6C4 = 4 × 15 = 60. So 252 - 66 = 186... check directly: 2W: 6C3×4C2 = 20×6 = 120; 3W: 6C2×4C3 = 15×4 = 60; 4W: 6C1×4C4 = 6. Sum = 186.

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