Question 933396
<pre>
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 {{{5!/e}}} = 44

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

Edwin</pre>