SOLUTION: There are 5 people and 5 different pairs of shoes. If each person chooses at random one right shoe and one left shoe how many combinations can be made in which no one gets a correc

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Question 933396: There are 5 people and 5 different pairs of shoes. If each person chooses at random one right shoe and one left shoe how many combinations can be made in which no one gets a correct pair.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
There are 5! ways they can choose the 5 pairs of right shoes.
For each of those 5! way of choosing a right shoe, there are !5
(5 subfactorial) ways they can all choose left shoes that do 
not match the right shoe they chose. Such choices are known as
"derangements":

!5 = integer part of  = 44

Answer: (5!)(!5) = (120)(44) = 5280 ways.

Edwin
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