what you say you know is incorrect
all 52 cards in a deck are different
How many possible distinct 5 card hands can be dealt from a standard 52 card deck? The order in which the cards are dealt doesn't matter.
I know it ISN'T 52 choose 5 because the cards have to be DISTINCT, or DIFFERENT.
2 answers
It is C(52,5), trust us
another approach:
suppose you had to pick them in a specific order,
then the number of ways would be 52x51x50x49x48
which is the same as 52! / 47! or P(52,5)
But the order does not matter, as you said, so we have to divide by 5! the number of arrangements that would all yield the same selection
thus getting 52!/47! ÷ 5! , which is 52!/(47!5!) = C(52,5) by definition.
another approach:
suppose you had to pick them in a specific order,
then the number of ways would be 52x51x50x49x48
which is the same as 52! / 47! or P(52,5)
But the order does not matter, as you said, so we have to divide by 5! the number of arrangements that would all yield the same selection
thus getting 52!/47! ÷ 5! , which is 52!/(47!5!) = C(52,5) by definition.
2 answers