Question

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

Answer 1

ANSWER

2730 groups

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:

$^nP_r=\frac{n!}{(n-r)!}$

Therefore, we have:

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