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

 Apr 10, 2020
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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  4C2 = 6 ways.

You need to get two of the four kings -- which also occurs in  4C2 = 6 ways.

You need to get none of the rest of the deck -- which occurs in  48C0 = 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  52C4 = 270725 ways -- and divide 36 by 270725 to get the answer.

 Apr 10, 2020

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