Question

4 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

1365

Explanation:

formula for combination

n!/r!(n-r)!

Answer 2

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
1365