Separate the 12 face cards from the rest of the deck. Assume that the remaining cards have been shuffled. Select THREE cards from the pile of face cards. How many ways are there of selecting one of each face card from the pile.

Second question: How many ways are there of selecting three of the same face cards (ie. 3 jack, 3 queens, 3 kings)

There are 4 Kings, 4 Queens, 4 Jacks.

It would appear there are 4^3=64 ways to select one of each.

If the order matters, use permutations. If the order does not matter use combinations.

n P m = n!/(n-m)!

n C m = n!/(m!*(n-m)!)


For your question, n is 12 and m is 3.

12!/9! Or 1320 ways to deal 3 cards from a deck of 12
The number of unique hands resulting is 220 --- 12!/(3!*9!)


The second question how many ways to get 3 of a kind from that deck.

The easiest was is to count the ways to pick the card NOT in the 3 of a kind.
There are 4 ways to get 3 jacks, same for Q and K.

Answer is 12.