TITLE: Poker Combinations: How many ways can you get 4 of the same suit in a hand of 5 cards?
QUESTION [7 upvotes]: The homework question is: in how many ways can we get exactly 4 cards of the same suit in a hand of 5 cards? (Order does not matter.)
Here is what I have: we need to pick two different suits, decide which suit will have 4 cards and which will have 1, pick 4 ranks for one suit, pick 1 for the other. That is, $$\binom{4}{2}\binom{2}{1}\binom{13}{4}\binom{13}{1}$$
Does this seem correct? Thanks!

REPLY [7 votes]: Your answer is correct.
Here is an alternate method:  Select one of the four suits, four of the thirteen cards from that suit, and one of the $39$ cards that is not of that suit, which yields 
$$\binom{4}{1}\binom{13}{4}\binom{39}{1}$$