Odds of quads, a full house and two pair

Five cards are dealt from a shuffled standard deck. Find the probabilities of being dealt (a) four of a kind, (b) a full house (three of one rank and two of another), and (c) exactly two pairs.

(a) $\tfrac{624}{2{,}598{,}960}\approx0.00024$; (b) $\tfrac{3{,}744}{2{,}598{,}960}\approx0.00144$; (c) $\tfrac{123{,}552}{2{,}598{,}960}\approx0.0475$. Counts: $13\cdot48$ for quads; $13\binom43\cdot12\binom42$ for a full house; $\binom{13}{2}\binom42^2\cdot44$ for two pair, all over $\binom{52}{5}$.