SOLUTION: a. How many ways are there to choose four fives from a standard 52-card deck? b. How many ways are there to choose one card from a standard 52-card deck without choosing any fives

Question 1098385: a. How many ways are there to choose four fives from a standard 52-card deck?
b. How many ways are there to choose one card from a standard 52-card deck without choosing any fives?
c. How many five-card hands (drawn from a standard 52-card deck) contain exactly four fives?
d. How many five-card hands (drawn from a standard 52-card deck) contain a four-of-a-kind?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
a. How many ways are there to choose four fives from a standard 52-card deck?
There are only 4 fives, so there is only 1 possible set of fives you can get..
There is only 1 such combination, and that is what I believe was meant by the question.
(If you cared what order the cards were received, there would be 4!=4*3*2=24 permutataions).

b. How many ways are there to choose one card from a standard 52-card deck without choosing any fives?
52-4=48 of the cards are not a five,
so there are 48 ways to choose one card from a standard 52-card deck without choosing any five.

c. How many five-card hands (drawn from a standard 52-card deck) contain exactly four fives?
As there is exactly 1 set of 4 fives, and 48 ways to choose the 5th card,
there are 1 X 48 = 48 five-card hands containing exactly four fives.

d. How many five-card hands (drawn from a standard 52-card deck) contain a four-of-a-kind?
There are 52/4=13 different "kinds of cards in a standard 52-card deck.
There are 48 five-card hands containing exactly four fives.
There are also
48 five-card hands containing exactly four aces,
48 five-card hands containing exactly four twos,
48 five-card hands containing exactly four threes,
48 five-card hands containing exactly four fours,
48 five-card hands containing exactly four sixes,
and so on.
Considering all 13 kinds of cards there are 13 X 48 = 624
card hands containing four-of-a-kind.

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