CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations
A board of 5 directors is to be formed from 7 men and 5 women such that it has at least 3 women. How many boards are possible?
There are 246 possible boards. Add the cases: 3 women and 2 men gives 10 × 21 = 210, 4 women and 1 man gives 5 × 7 = 35, and 5 women gives 1. The total is 246; 210 counts only the first case.
- A246Correct
- B120
- C396
- D210
Explanation
Cases: 3 women and 2 men = 5C3×7C2 = 10×21 = 210; 4 women and 1 man = 5C4×7C1 = 5×7 = 35; 5 women = 1. Total = 210+35+1 = 246. Option 210 omits the 4-woman and 5-woman cases.
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