binomial distrubution

Question

how many 5 card hands can be dealt from a standard deck of 52 cards?

Answer 1

There’s a formula for the number of ways of choosing k out of n things. You should look it up in your textbook (or other learning material). It’s

C(n,k) = (n!) / [ (k!) * (n-k)! ]

Just plug in the numbers and do the arithmetic.

Answer 2

52!/{(47!)(52-47)!}

= 52!/(47! 5!)

= 52 X 51 X 50 X 49 X 48 / (5 X 4 X 3 X 2 X 1)

= 311,875,200 / 120

= 2,598,960

Note in line 3 we cancelled 47!/47!, since 52! = 52 X 51 X 50 X 49 X 48 X 47!