AMC 10 2021b Problem 4

At a math contest, $57$ students are wearing blue shirts, and another $75$ students are wearing yellow shirts. The $132$ students are assigned into $66$ pairs. In exactly $23$ of these pairs, both students are wearing blue shirts. In how many pairs are both students wearing yellow shirts? $\textbf{(A)} ~23 \textbf{(B)} ~32 \textbf{(C)} ~37 \textbf{(D)} ~41 \textbf{(E)} ~64$