You are dealt five cards from an ordinary deck of 52 playing cards. In how many ways can you get a full house and a five-card combination containing two jacks and three aces?
Full house = 3744, that specific full house = 24
To start, let's review what a standard deck of cards looks like: 13 ordinal cards (Ace, 2-10, Jack, Queen, King) - 1 of each ordinal in each of 4 suits (spades, clubs, hearts, diamonds), and so there are 52 cards:
The first thing we need is 3 cards of the same ordinal, so we can express that as taking 1 of the 13 ordinals and getting 3 of 4 of them:
The next thing we need is 2 cards from the same ordinal and this ordinal has to be different than the one we just chose from, so that looks like:
And now we multiply them together:
This is the number of full houses we can draw in a game of 5-card poker.
For the number of hands we can draw getting specifically 2 Jacks and 3 Aces, we calculate that this way - we only need to concern ourselves with picking out the number of cards of the 4 available in each of the listed ordinals, and so we get: