Multinomial Coefficient

A notation used to divide combinations into smaller sub-boxes.

Notation

$$C_{a,b,c}^n=\left(\genfrac{}{}{0ex}{}{n}{a,b,c}\right)=\frac{5!}{a!b!c!}$$

Where:

• $a+b+c=n$

Example

Split a group of 12 people into 3 groups of 2 people, 5 people and 5 people

Soln

$$\frac{1}{2!}\left(\genfrac{}{}{0ex}{}{12}{2,5,5}\right)=\frac{12}{2!2!5!5!}$$

With the $\frac{1}{2!}$ corresponding to repeated groups