TITLE: 10 distinguishable letters to 5 people, with each person getting 2
QUESTION [0 upvotes]: How many ways can we send 10 distinguishable letters to 5
people such that each person gets exactly 2 letters.
Any help would be appreciated

REPLY [1 votes]: Put the letters in order, so that the first two letters will go to Alice, the next two will go to Bob, the next two to Charlie and so on.  There are 10! ways to order the letters thus.
But this counts each possibility $2^5$ times, since Alice's letters could be placed in either of two orders, so could Bob's, so could Charlie's, and so on.  
So the answer is $\frac{10!}{2^5}$ = 113400
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