Question

Choosing a Team In how many ways can a squad of$4$relay runners be chosen from a track team of$8$runners?

Short answer

The ways are$1680.$

Step-by-step solution

Step 1. Given information.

Number of runners $4$and numbers of runners in a track team are$8.$

Step 2. Calculation.

The ways can a squad runners be chosen is -

$$\begin{gathered} C\left(8,4\right)=\frac{8!}{\left(8-4\right)!} \\ =\frac{8\times 7\times 6\times 5\times 4!}{4!} \\ =8\times 7\times 6\times 5 \\ =1680. \end{gathered}$$