1. The problem statement, all variables and given/known data Suppose b | a!(n-a)! and prove that b | n! 2. Relevant equations m | n <=> n = am 3. The attempt at a solution b | a!(n-a)! ,so that a!(n-a)! = bs, so that a!(n-a)!(nCa) = bs(nCa) (nCa is a combinations of n items) n! = bs(nCa) And so b is obviously a divisor of n!