CA Foundation · Quantitative Aptitude · Permutations and Combinations
From 8 men and 6 women, a committee of 6 is to be formed with more women than men, and Mrs. Iyer, one of the women, must be on it. In how many ways can this be done?
The committee can be formed in 321 ways. With Mrs. Iyer fixed, count committees with 4, 5 or 6 women in total: 280 + 40 + 1 = 321.
- A321Correct
- B280
- C441
- D1001
Explanation
Mrs. Iyer is fixed; choose 5 others from 8 men and 5 remaining women. Women must total 4, 5 or 6. Total 4 women: 5C3 x 8C2 = 10 x 28 = 280. Total 5: 5C4 x 8C1 = 40. Total 6: 5C5 = 1. Sum = 321. The option 280 counts only the 4-woman case.
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