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QUESTION

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

194,580 unique hands

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.