Finding the number of blue socks

EasyProbability Combinatorics~4m

A drawer holds $3$ red socks and $n$ blue socks. Two socks are drawn uniformly at random without replacement, and the probability that both are red is $\tfrac12$ . Find $n$ .

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$\mathbb{P}(\text{both red})=\binom{3}{2}/\binom{n+3}{2}=6/((n+3)(n+2))$ .
Set it to $1/2$ : $(n+3)(n+2)=12$ .

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Finding the number of blue socks

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