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The Burning Question Part 2 An extension of the previous thread, which grew quite long.

Quoting Prashant from the last thread, "Number of ways to compare two applicants from a pool of 10,500 is 10500(C)2 = (10500!)/(2!*(10498!))"
I don't need to win the USAMO to know that's a lot of ways.
What a lively