What is the value of multinomial of 3, 5 and 7 ?

Number Theory Level 3

This problem's question is what is the value of the multinomial of the list of integers 3, 5 and 7?

The definition of the multinomial of list \text{list} is ( ∑ i ∈ list i ) ! ∏ i ∈ list i ! \frac{(\sum _{i\in \text{list}} i)!}{\prod _{i\in \text{list}} i!} .


The answer is 360360.

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1 solution

∑ i ∈ { 3 , 5 , 7 } i ∏ i ∈ { 3 , 5 , 7 } i ! ⇒ 15 ! 3 ! 5 ! 7 ! ⇒ 360360 \frac{\sum _{i\in\{3,5,7\}} i}{\prod _{i\in \{3,5,7\}} i!} \Rightarrow \frac{15!}{3!\, 5!\, 7!} \Rightarrow 360360

If a binomial is the count of the number of different ways of selecting n n things (and, of course, the non-selection of the other m − n m-n things) from a total of m m things, then the multinomial is the . . . . ....

This applies to another of my problems.

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