Question

Sam is the captain of an academic team in the class. A teacher will choose 6 of the 25 students in the class to be on an academic team. How many ways can 6 students be chosen as a team from this class given that Sam must be one of those students?

Answer 1

42,504 ways to choose a team.

Explanation:

The order in which the students are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

In this question:

Sam

And 5 students from the remaining 24.

Then

`C_(24,5) = (24!)/(5!(24-5)!) = 42504`

42,504 ways to choose a team.