If 12 people are to be divided into 3 committees of respective sizes 3, 4, and 5, how many divisions are possible?

# If 12 people are to be divided into 3 committees of respective sizes 3, 4, and 5, how many divisions are possible?

J
Asked by 2 years ago
240 points

If 12 people are to be divided into 3 committees of respective sizes 3, 4, and 5, how many divisions are possible?

If 12
jeffp

### 1 Answer

Answered by 2 years ago
8.7k points

For this type of problem we use the multinomial coefficient,

$$\begin{pmatrix} 12 \\ 3,4,5 \end{pmatrix} = \frac{12!}{3! 4! 5!} = 27720$$

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Asked: 2 years ago