Mock AIME 2 2010 Problems/Problem 3
Problem
Five gunmen are shooting each other. At the same moment, each randomly chooses one of the other four to shoot. The probability that there are some two people shooting each other can be expressed in the form 
, where 
are relatively prime positive integers. Find 
.
Solution 1(PIE)
Let the five people be 
and 
. Let 
denote the event of 
and 
shooting each other and 
through 
similarly. Then, 
.
