SOLUTION: 11) In the game of poker, a typical hand consists of 5 cards, drawn for an ordinary pack of 52 playing cards, without replacement. Different combinations of cards in your hand dete

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Question 771114: 11) In the game of poker, a typical hand consists of 5 cards, drawn for an ordinary pack of 52 playing cards, without replacement. Different combinations of cards in your hand determine whether you win.
a) How many ways can five cards be dealt, from a pack of 52 cards?
b) A possible winning combination is to have 4 of the same kind (i.e. all of the Queens). If a single hand is dealt, what is the probability of the hand having all 4 Aces?
c) What is the probability of having 4 of a kind of any card?
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
11) In the game of poker, a typical hand consists of 5 cards, drawn for an ordinary pack of 52 playing cards, without replacement. Different combinations of cards in your hand determine whether you win.
a) How many ways can five cards be dealt, from a pack of 52 cards?
Combinations of 52 cards taken 5 at a time.

C(52,5) = 2598960

b) A possible winning combination is to have 4 of the same kind (i.e. all of the Queens). If a single hand is dealt, what is the probability of the hand having all 4 Aces?
Choose all the aces 1 way and the 5th card one of the 48 non-aces.

That's 1×48 or 48 ways out of 2598960 or 48%2F2598960 = 1%2F54145 ≈ 0.00001846892603

c) What is the probability of having 4 of a kind of any card?

Each is the same as 4 aces, so it's 13 times as likely, so we multiply by 13
  13*1%2F54145 = 13%2F54145 = 1%2F4165 ≈ 0.0002400960384.

Edwin