CA Foundation · Quantitative Aptitude · Permutations and Combinations
From 8 men and 6 women, a committee of 6 is to be formed so that it has more women than men, and Mrs. Iyer, one of the women, must be on the committee. In how many ways can this be done?
The count is 321, from 280 + 40 + 1 ways for 4, 5 or 6 women including Mrs. Iyer.
- A1001
- B1456
- C1176
- D756Correct
Explanation
Mrs. Iyer is fixed, so choose 5 more from 8 men and 5 other women with women total greater than men. Total women must be 4, 5 or 6 (men 2, 1, 0). Women 4 means 3 more from 5: 5C3 x 8C2 = 10 x 28 = 280. Women 5 means 4 more: 5C4 x 8C1 = 5 x 8 = 40. Women 6 means 5 more: 5C5 = 1. Total 321. This does not match any option, so the key is flawed.
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