Question

If we remove all of the queens from a 52-card deck, how many unique four card combinations can we have?

Answer 1

`194,580` unique hands

Explanation:

If thee 4 queens are removed, we will have 48 cards to choose from.

There are `48xx47xx46xx45` different combinations of cards which are possible, but in this case the order is not important, we are only interested in the actual cards in a hand of 4.

4 cards can be arranged in `4!` ways.

THe number of combinations is therefore `(48xx47xx46xx45)/(4!)`

This can also be written as `(48!) /(4! xx 44!)`

`194,580` unique hands.