Compute the multinomial coefficient
Jelly, 7 6 bytes

;_/!:/


Look ma, no Unicode! This program takes a single list as input, with n at its first index.

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How it works

;_/!:/ Input: A (list)

 _/    Reduce A by subtraction. This subtracts all other elements from the first.
;      Concatenate A with the result to the right.
   !   Apply factorial to all numbers in the resulting list.
    :/ Reduce the result by division. This divides the first element by the others.