Question

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

Answer 1

`2,118,760` 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`