Question

If a 5-card hand is dealt from a deck of 52 cards, how many hands have cards that are all the same colour?

Answer 1

131,560

Explanation:

There are 26 black cards and 26 red cards. We can draw 5 cards from the population of 26 cards of either colour, then multiply by 2 to account for the fact that this works with both black and red.

A poker hand is a combination, the general formula of which is:

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

and so we have:

`2xx(26!)/((5!)(21!))=2xx65,780=131,560`