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14.Probability
easy
A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man ?
A
$\frac{2}{3}$
B
$\frac{2}{3}$
C
$\frac{2}{3}$
D
$\frac{2}{3}$
Solution
The total number of persons $=2+2=4 .$ Out of these four person, two can be selected in $^{4} C _{2}$ ways.
One man in the committee means that there is one woman. One man out of $2$ can be selected in $^{2} C _{1}$ ways and one woman out of $2$ can be selected in $^{2} C _{1}$ ways.
Together they can be selected in $^{2} C _{1} \times^{2} C _{1}$ ways.
Therefore $P$ (One man) $=\frac{^{2} C _{1} \times^{2} C _{1}}{^{4} C _{2}}$ $=\frac{2 \times 2}{2 \times 3}=\frac{2}{3}$
Standard 11
Mathematics
