# A Committee of Two Persons is Selected from Two Men and Two Women. What is the Probability that the Committee Will Have (I) No Man? - Mathematics

A committee of two persons is selected from two men and two women. What is the probability that the committee will have  no man?

#### Solution

Total number of people = 2 + 2 = 4
Out of these four people, two can be selected in 4C2  = 6 ways.

No man in the committee of two means that there will be two women in the committee.
Out of two women, two can be selected in 2C2 = 1 way.
∴ P(no man) = $\frac{^{2}{}{C}_2}{^{4}{}{C}_2} = \frac{1}{2 \times 3} = \frac{1}{6}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 25.1 | Page 47