A committee of 5 people is to be chosen from a group of 6 men
MATHEMATICS
JAMB 2023
A committee of 5 people is to be chosen from a group of 6 men and 4 women. How many committees are possible if there is to be a majority of women?
- A. 60
- B. 15
- C. 66
- D. 4
Correct Answer: C. 66
Explanation
If the majority are women implies that:
3 Women and 2 Men Or 4 Women and 1 Man
= \(^4C_3 \times^6C_2+^4C_4\times^6C_1\)
= \(4 \times 15 + 1 \times 6\)
= 60 + 6 = 66
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