Sum of Multinomial Coefficients

Sum of Multinomial Coefficients

## Formula

For:

$$(x_1+x_2+\cdots+x_k)^n$$

the sum of all multinomial coefficients is obtained by putting:

$$x_1=x_2=\cdots=x_k=1$$

Therefore:

$$\sum\frac{n!}{r_1!r_2!\cdots r_k!}=k^n$$

where:

$$r_1+r_2+\cdots+r_k=n$$

## Usage

- Used to find the sum of all coefficients in a multinomial expansion.