I am stomped on the following question
How many different ways are there to draw $6$ cards from a standard deck of cards and obtain $4$ kings and $2$ jacks? (The Answer is $6$)
I believe I am starting the question all wrong since I am doing this for
How many different ways are there to draw $6$ cards from a standard deck of cards
No. of ways = $\frac{52!}{46!6!} $
Any suggestions on how I would solve this problem ?
Best Answer
I believe the total number of hands is completely irrelevant for answering this question. All you need to know is that you need 6 cards. 4 cards need to be kings. 4 cards need to be jacks. You only have 4 kings, and you only have 4 jacks. The number of ways you can draw 4 kings out of a set of 4 kings is 4C4 = 1. The number of ways you can draw 2 jacks from a set of 4 is 4C2 = 6.
This makes your answer 4C4 * 4C2 = 1 * 6 = 6