Question

How many different committees of six people can be selected from nine people?

Answer 1

ANSWER

$84$

EXPLANATION

To find the number of committees of six people that can be selected from nine people, we apply Combination:

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

Therefore, we have:

$\begin{gathered} ^9C_6=\frac{9!}{(9-6)!6!} \\ \Rightarrow\frac{9\cdot8\cdot7\cdot6!}{3!6!} \\ \Rightarrow\frac{9\cdot8\cdot7}{3\cdot2\cdot1} \\ \Rightarrow84 \end{gathered}$

Hence, there are 84 different ways of selecting.