[Math] HW Probability Problem

Question

How many different bridge hands are possible containing five spades, three diamonds, threee clubs, and two hearts?

Please provide some helpful hints as I am unfamiliar with most card games.

Answer 1

Not much card knowledge is needed here, only that a bridge hand is any collection of $13$ cards. These are chosen from the standard $52$-card deck, which has $13$ spades, $13$ hearts, $13$ diamonds, and $13$ clubs. The $13$ spades are all different, as are the $13$ hearts, and so on.

For counting the hands of the kind described, note that the $5$ spades can be chosen in $\binom{13}{5}$ ways. For every way of choosing the spades, there are $???$ ways of choosing the $3$ diamonds from the $13$ available. And for every way of choosing the spades and diamonds, there are $???$ $\dots$.