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there are 10 students, I pick 3 for a field trip how many ways can I choose. HINT: combination

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How many ways can a committee of three be chosen from a group of ten people? How many ways are there to choose a president, secretary, and treasurer.

I know that on the first part I have to use the combination formula since order doesn't matter. Then !!(−)!→10!3!(10−3)!
n
!
r
!
(
n

r
)
!

10
!
3
!
(
10

3
)
!
= 120.

The second part requires order meaning that I need to use the permutation formula !(−)!
n
!
(
n

r
)
!

10!(10−3)!
10
!
(
10

3
)
!
= 720.
by