$3$ cards are chosen at random from a standard $52$-card deck. What is the probability that they form a pair? (A $3$-card hand is a `pair' if two of the cards match in rank but the third card is different. For example, $668$ is a pair, but $999$ is not.)
Any hints are greatly appreciated.
Best Answer
A pair of say Aces, then $\binom{4}{2}\cdot \binom{48}{1}$, and there are $13$ ranks, so choose a rank first that is to have $\binom{13}{1}$, thus the probability is: $\dfrac{\binom{13}{1}\cdot \binom{4}{2}\cdot \binom{48}{1}}{\binom{52}{3}}$