CA Foundation · Quantitative Aptitude · Permutations and Combinations
A company in Hyderabad has 6 managers and 4 analysts. A committee of 4 is to be formed with at most 1 analyst. In how many ways can this be done?
The committee can be formed in 95 ways, by adding the cases of no analyst (15 ways) and exactly one analyst (80 ways).
- A135Correct
- B210
- C15
- D120
Explanation
At most 1 analyst means 0 or 1 analyst. With 0 analysts: 6C4 = 15. With 1 analyst: 4C1 x 6C3 = 4 x 20 = 80. Total = 15 + 80 = 95. Check by complement: total 10C4 = 210; with 2 analysts 6C2 x 4C2 = 90... that is 15 x 6 = 90; with 3 analysts 4C3 x 6 = 24; with 4 analysts 1; sum 115; 210 - 115 = 95. So correct is 95, and no option matches.
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