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Question
A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?
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Solution
A committee of 3 people is to be constituted from a group of 2 men and 3 women.
∴ Number of ways =\[{}^2 C_0 \times^3 C_3 +^2 C_1 \times^3 C_2 + {}^2 C_2 \times^3 C_1 = 1 + 2 \times 3 + 3 \times 1 = 10\]
Number of committees consisting of 1 man and 2 women =\[{}^2 C_1 \times^3 C_2 = 6\]
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