Question

a teacher is holding tryouts for a school play. there are 15 students trying out for 7 parts in the play each student can play each part. in how many ways can the teacher select the students?

Answer 1

6,435

Explanation:

To find the number of ways the teacher can select the students, we can use the combination formula.

`_(n)C_(k)=(n!)/(k!(n-k)!)`

n = 15

k = 7

Now let's plug it in.

`_(n)C_(k)=(n!)/(k!(n-k)!)`

`_(15)C_(7)=(15!)/(7!(15-7)!)`

`_(15)C_(7)=(15!)/(7!8!)`

`_(15)C_(7)=6,435`

So there are 6,435 ways that the teacher can select the students.