CA Foundation · Quantitative Aptitude · Permutations and Combinations
A Mumbai firm must form a team of 5 from 7 men and 5 women so that the team has at most 2 women. In how many ways can this be done?
The answer is 546. Add the cases with 0, 1 and 2 women: 7C5 = 21, 5C1 x 7C4 = 175 and 5C2 x 7C3 = 350. The total is 546, which matches 12C5 = 792 minus 246 teams with three or more women.
- A546Correct
- B441
- C596
- D350
Explanation
Cases: 0 women: 7C5 = 21. 1 woman: 5C1 x 7C4 = 5 x 35 = 175. 2 women: 5C2 x 7C3 = 10 x 35 = 350. Total = 21 + 175 + 350 = 546. Check: 12C5 = 792; at least 3 women = 5C3x7C2 + 5C4x7C1 + 5C5 = 210+35+1 = 246; 792-246 = 546. Option 441 omits... the 0-women case and adds wrongly; 596 miscounts.
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