# 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? - Mathematics

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?

#### 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 =${}^2 C_1 \times^3 C_2 = 6$

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Exercise 17.2 | Q 20 | Page 16