# math - combinations

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Each hand in the game of bridge has 13 cards dealt from a regular deck of 52 cards.

a) How many different bridge hands are possible?
b) How many different bridge hands have all pour aces in them?
c) How many different bridge hands have no aces in them?

I figured out part A, but am confused about the rest..
52nCr13 = 6.35 x 10^11 hands

• math - combinations -

a) choose 13 from 52 = C(52,13) = 6.35 x 10^11

b) you have the four aces, that leaves 9 other cards from the remaining 48
so C(48,9) = 1677106640

c) imagine the deck with no aces, that would be 48 to choose from, but you still want 13 cards
C(48,13) = 1.929x10^11

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Can someone please explain this to be, so that I can understand this problem?

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