A committee of two persons is selected from two men and two women. probability that committee will h

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14.Probability

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

A

$\frac{1}{6}$

B

$\frac{1}{6}$

C

$\frac{1}{6}$

D

$\frac{1}{6}$

Solution

The total number of persons $=2+2=4 .$ Out of these four person, two can be selected in $^{4} C _{2}$ ways.

No men in the committee of two means there will be two women in the committee.

Out of two women, two can be selected in $^{2} C _{2}=1$ way.

Therefore $P$ (no man) $=\frac{^{2} C _{2}}{^{4} C _{2}}$ $=\frac{1 \times 2 \times 1}{4 \times 3}$ $=\frac{1}{6}$

Standard 11

Mathematics

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