Question

A teacher is selecting students for a trivia bowl. If there are nine interested students and a trivia bowl team consists of three players, how many different teams can the teacher select? A 24 B. 84 C. 252 D. 504

Answer 1

The number of different combinations of k elements in a set of n elements, is:

`(n!)/(k!(n-k)!)`

If we want to select three players from a group of 9 students, then the amount of different teams will be given by:

`\begin{gathered} (9!)/(3!(9-3)!)=(9!)/(3!\cdot6!) \\ =(9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2)/(3\cdot2\cdot6\cdot5\cdot4\cdot3\cdot2) \\ =(9\cdot8\cdot7)/(3\cdot2) \\ =(9)/(3)\cdot(8)/(2)\cdot7 \\ =3\cdot4\cdot7 \\ =84 \end{gathered}`

Therefore, the total amount of different teams that can be selected, is:

`84`