A committee of 5 people is to be chosen from a ... - JAMB Mathematics 2023 Question
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 option: c
The number of ways to choose a committee with 3 women and 2 men is given by \(^4C_3 \times ^6C_2\). Similarly, the number of ways to choose a committee with 4 women and 1 man is given by \(^4C_4 \times ^6C_1\).
\[ ^4C_3 \times ^6C_2 + ^4C_4 \times ^6C_1 = 4 \times 15 + 1 \times 6 = 66 \]
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