If you have 2n socks in a drawer, n white and n black, and you reach in to choose 2 socks at random,
How many ways are there to choose? For this I got 2(n^2-n)
How many of these ways result in getting a pair of the same color?
Write a simple closed form formula in terms of n for the chance choosing a matching pair of socks from a drawer with n white and n black socks.
Best Answer
There are $2n$ socks. You have a choice of $2n$ for the first and then $2n-1$ for the second, but order doesn't matter. That's $\frac{2n (2n-1)}{2}$, which is $\dbinom{2n}{2}$.
For each colour count the ways to select two socks. That is $\dbinom{\Box}{2}+\dbinom{\Box}{2}$, or $\underline{\qquad}$
Divide and simplify.