Question

How many distinct committees of 3 people can be formed if the members are drawn from a pool of 15 people?

Answer 1

2730 groups

Step-by-step explanation

We want to find the number of distinct committees of 3 can be formed from a pool of 15 members.

To do this, we apply combination.

That is:

`^nP_r=(n!)/((n-r)!)`

Therefore, we have:

`\begin{gathered} ^(15)P_3=(15!)/((15-3)!)=(15!)/(12!) \\ =(15\cdot14\cdot13\cdot12!)/(12!) \\ =15\cdot14\cdot13 \\ =2730\text{ groups} \end{gathered}`