Answer
The number of ways to select 6 people out of 13 = $13_{{C}{_{6}}}$ = 1716
Work Step by Step
Total number of people who have volunteer for test = 13
Number of people needed for test = 6
To find the number of ways to select 6 people out of 13 we use the combination formula $n_{{C}{_{r}}}$ = $\frac{n!}{(n - r)! r!}$
The number of ways to select 6 people out of 13 = $13_{{C}{_{6}}}$ = $\frac{13!}{(13 - 6)! 6!}$
= $\frac{13!}{7! . 6!}$
= $\frac{13\times12\times11\times10\times9\times8\times7!}{7! . (6\times5\times4\times3\times2\times1)}$
= $\frac{13\times12\times11\times10\times9\times8}{6\times5\times4\times3\times2\times1}$
= 1716
