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2023

Mathematics

67ca00ce0c643c71d77dee1f

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: 66

Explanation

If the majority are women implies that: 3 Women and 2 Men Or 4 Women and 1 Man = 4C3 × 6C2 + 4C4 × 6C1 = 4 × 15 +1 × 6 = 60 + 6 = 66

If the majority are women implies that: 3 Women and 2 Men Or 4 Women and 1 Man = 4C3 × 6C2 + 4C4 × 6C1 = 4 × 15 +1 × 6 = 60 + 6 = 66
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