The number of different combinations of k elements in a set of n elements, is:
[tex]\frac{n!}{k!(n-k)!}[/tex]If we want to select three players from a group of 9 students, then the amount of different teams will be given by:
[tex]\begin{gathered} \frac{9!}{3!(9-3)!}=\frac{9!}{3!\cdot6!} \\ =\frac{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2}{3\cdot2\cdot6\cdot5\cdot4\cdot3\cdot2} \\ =\frac{9\cdot8\cdot7}{3\cdot2} \\ =\frac{9}{3}\cdot\frac{8}{2}\cdot7 \\ =3\cdot4\cdot7 \\ =84 \end{gathered}[/tex]Therefore, the total amount of different teams that can be selected, is:
[tex]84[/tex]
