A committee of 3 members is to be selected out of 3 men and 2 women What is the probability that the committee has at least one woman ?

A committee of 3 members is to be selected out of 3 men and 2 women What is the probability that the committee has at least one woman ?
1). $\frac{1}{10}$
2). $\frac{9}{20}$
3). $\frac{9}{10}$
4). $\frac{1}{20}$

Solution

The number of ways = Two men and one woman + One men and two women
$= \\frac{^3C_2 \\times ^2C_1}{^5C_3} + \\frac{^3C_1 \\times ^2C_2}{^5C_3}$

$= \\frac{6+3}{20}$

$= 9/20$

Hence, the correct option is C.

correct option is C.

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