Chance of being dealt three of a kind

Five cards are dealt from a well-shuffled $52$-card deck. What is the probability that the hand is exactly three of a kind, meaning three cards share one rank and the other two cards have two further, different ranks?

$88/4165\approx0.0211$. Choose the triple's rank and suits ($13\cdot4$), the two other ranks ($\binom{12}{2}=66$) and a suit for each ($4^2$). That gives $54{,}912$ hands out of $\binom{52}{5}=2{,}598{,}960$.