SOLUTION: From a deck of 52 playing cards, how many different ways can a hand of 5 cards contain four of a kind? (4 cards have the same number and the 5th card of some other number and order

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Question 853556: From a deck of 52 playing cards, how many different ways can a hand of 5 cards contain four of a kind? (4 cards have the same number and the 5th card of some other number and order is important).
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
From a deck of 52 playing cards, how many different ways can a hand of 5 cards contain four of a kind? (4 cards have the same number and the 5th card of some other number and order is important).
A.  If order in which they are dealt is NOT important:

Choose the rank of the 4 of a kind in 13 ways.
Choose the 5th card any of the other 48 cards.

That's 13×48 = 624 possible four of a kind hands, where
the order in which they are dealt is NOT important.

B.  If order in which they are dealt IS important:

Each of the 624 hands can be dealt in 5! or 120 different orders.

Answer: 624×5! = 624×120 =  74880

Edwin
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