How many different 7-card hands include the ace and king of spades?

1 Answer
MathFact-orials.blogspot.com
May 21, 2018

2,118,7602,118,760 ways

Explanation:

We start with a standard 52 card deck and pull out the Ace and King of Spades and set them aside.

We now need 5 more cards from the remaining 50. This is a combination question, and so we use:

C_(n,k)=((n),(k))=(n!)/((k!)(n-k)!) with n="population", k="picks"

((50),(5))=(50!)/((45!)(5!))=(50xx49xx48xx47xx46)/120=2,118,760

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