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There are $\mathrm{n}$ socks in a drawer, of which 3 socks are red. If 2 of the socks are chosen randomly and the probability that
both selected socks are red is $\frac{1}{2}$, then what is the value of n?
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both selected socks are red is $\frac{1}{2}$, then what is the value of n?
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The correct answer is:
4
Number of socks $=\mathrm{n}$ Number of red socks $=3$
Given, $\frac{{ }^{3} C_{2}}{{ }^{n} C_{2}}=\frac{1}{2}$
$\Rightarrow{ }^{\mathrm{n}} \mathrm{C}_{2}=3 \times 2=6$
$\Rightarrow \mathrm{n}=4$
Given, $\frac{{ }^{3} C_{2}}{{ }^{n} C_{2}}=\frac{1}{2}$
$\Rightarrow{ }^{\mathrm{n}} \mathrm{C}_{2}=3 \times 2=6$
$\Rightarrow \mathrm{n}=4$
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