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