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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations

A committee of 5 is to be formed from 7 men and 5 women so that it contains at least 2 women. In how many ways can this be done?

The committee can be formed in 596 ways. Total selections are 12C5 = 792. Cases with no woman (21) or exactly one woman (175) are excluded, totalling 196. So 792 minus 196 gives 596, which matches the direct sum of the 2, 3, 4 and 5 women cases.

  1. A792
  2. B441
  3. C596Correct
  4. D350

Explanation

Total 12C5 = 792. Subtract cases with fewer than 2 women. 0 women: 7C5 = 21. 1 woman: 5C1×7C4 = 5×35 = 175. Invalid = 196. Answer = 792-196 = 596. Direct check: 2W: 10×35=350; 3W: 10×21=210; 4W: 5×7=35; 5W: 1; total 596. Option 441 is 792-350 (wrong subtraction).

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