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icantadd
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Homework Statement
Suppose b | a!(n-a)! and prove that b | n!
Homework Equations
m | n <=> n = am
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!