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- Division of Factorials 12 answers
Let $a_1, a_2, a_3,...,a_n$ be $n$ positive integers and if $a=a_1+a_2+a_3+...+a_n$. Prove that $a_1!a_2!a_3!...a_n! | a!$
Factorial of a sum of $n$ numbers is divisible by product of factorial of these numbers.