If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability of getting two queens and two kings.

Guest Apr 10, 2020

#1**0 **

Divide the deck into three groups, the queens, the kings, and the rest of the deck.

You need to get two of the four queens -- which occurs in _{4}C_{2} = 6 ways.

You need to get two of the four kings -- which also occurs in _{4}C_{2} = 6 ways.

You need to get none of the rest of the deck -- which occurs in _{48}C_{0} = 1 way.

Multiplying these together gives you the various ways that you can get these four cards = 6 x 6 x 1 = 36 ways.

To find the probability that this will occur, we need to find the number of ways that 4 cards can be chosen from 52 cards -- which occurs in _{52}C_{4} = 270725 ways -- and divide 36 by 270725 to get the answer.

geno3141 Apr 10, 2020