Question

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

Answer 1

`84`

Step-by-step explanation

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

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

Therefore, we have:

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

Hence, there are 84 different ways of selecting.