Answer:
192 total ways
Step-by-step explanation:
This time, we have already 2 selected kings, therefore we must find the remaining 3 cards.
There are two general ways to do this:
Case 1: you draw two of some other matching cards and another king
Case 1 - K + X + X where K is a King and X is some other card than a King. So there are 2 Ks to draw. Then there are 12 other cards that are not from the king, and since you get two of them it would be 2 taken from 4:
4C2 = 4! / (2! * (4-2)!) = 6
Therefore there are 6 different arrangements of the two.
So 2 * 12 * 6 = 144 total ways to do this.
Case 2: you draw three of some other matching cards
Case 2 - X + X + X where the Xs are all non-king cards. So 12 cards to choose from, and then calculate 3 taken from 4:
4C3 = 4! / (3! * (4-3)!) = 4
Therefore there are 4 different arrangements of the three. So 12 * 4 = 48 total ways to do this.
Which means that:
144 + 48 = 192
There are 192 total ways to get a full house when you start with two kings.
