I don't know what the hell I was thinking. My recursion doesn't work because after the first person chooses a name, although there are n-1 names left, it is not the same as n-1 people choosing n-1 names because one of their names may already be taken.


This is a little better than the math geek problem because since there are only 10 names, you have to use inclusion-exclusion or your answer will be off. If you assume indpendence or you will be off by 2%.