Question

how many ways can you choose 3 volunteers from 12 students

Answer 1

You pick the ones that don't want to participate.

Answer 2

its 12C3=220

Answer 3

For first position, there are 12 ways to choose, for second, since one is already selected, there are 11 way to choose, and, again, since another one is already selected, there are 10 ways to choose for third position, hence \(12\times11\times10=1320\).

Because order doesn't matter, we need to divide it by how many ways three volunteer can be arranged.

There is three selected volunteers, so we have three ways for first posiiton, two ways for second, one for third, so we need to divide \(1320\) , by \(3\times2\times1=6\):
\[^{12}C_{3}=\dfrac{12!}{9!~3!} = \dfrac{1320}{6} = \boxed{220}\]

Answer 4

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