Question

There are 14 people sitting at a coffee shop. How many ways can the shop hand out 6 surveys for the customers to complete?

Answer 1

Explanation

From the question,

• There are 14 people sitting at a coffee shop

,

• 6 surveys are to be handed out

This can be carried out as follows:

$\begin{gathered} ^nP_r=\frac{n!}{(n-r)!} \\ ^{14}P_6=\frac{14!}{(14-6)!}=\frac{14!}{8!} \\ =\frac{14\times13\times12\times11\times10\times9\times8!}{8!} \\ =14\times13\times12\times11\times10\times9 \\ =2162160\text{ }ways \end{gathered}$

Hence, this can be done in 2162160 ways.