Question

students from a class of 15 are going to be chosen to be on the dance committee. Find the number of different 4-person committees that can be made.

Answer 1

we know that

The formula for combinations is

`C=n!/[(n-r)!*r!]`

where

`n` is the total number of objects you choose from

`r` is the number that you choose to arrange

in this problem

`n=15` students

`r=4` students

`C=15!/[(15-4)!*4!]` →
`C=15!/[11!*4!]` →
`(15*14*13*12*11!)/(11!*4*3*2*1)`

`C=(15*14*13*12)/(24)` →
`C=1365`

the answer is

1,365