Question

There are 6 athletes on a cross country team. At a photoshoot, 2 of the athletes need to be chosen and arranged in the front row. In how many ways can this be done?

Answer 1

Given:

Total athletes = 6

Chosen and arranged in row = 2

Find-:How many ways can this be done

Sol:

Chosen 2 athletes.

Combination without repetition is:

$=\frac{(n+r-1)!}{r!(n-1)!}$

Where ,

$\begin{gathered} n=6 \\ \\ r=2 \end{gathered}$

So,

$\begin{gathered} =\frac{(6+2-1)!}{2!(6-1)!} \\ \\ =\frac{7!}{2!\times5!} \\ \\ =\frac{7\times6\times5!}{2\times1\times5!} \\ \\ =7\times3 \\ \\ =21 \end{gathered}$

So total 21 ways