Question

how many 5 card hands have no spades?

Answer 1

As we know that a standard 52 deck of cards have four suits clubs(13 cards), diamonds(13 cards), hearts(13 cards) and spades(13 cards).

The given question is how many 5 hand cards have no spades i.e. if 5 cards are dealt then how many times there will be no spades in those 5 cards.

Now we know that a standard deck have 13 spades if we have no spades then the cards are either clubs, diamonds or hearts i.e. those 5 cards must come from the other (13+13+13)=39 cards.

That means to get no spades the cards must come from the other 39 cards. Now the number of ways that can happen is

Hence 575757 '5' hand cards will have no spades.