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At a certain high school, the Prom Committee is going to choose new members. There are 7 students from the Junior class and 10 students from the Senior class who are willing to be new members. In how many ways can 8 new members be chosen if more than 5 must be from the Senior class?

Respuesta :

We have:

7 students from the junior class

10 students from the senior class

So:

We need 5 from the senior class

There are a total of 17 students so. the ones that can be any grade are:

[tex]17-6=11[/tex]

since you need a total of 8 students in the committee and 5 have to be in the categories described above, that leaves:

[tex]8-6=2[/tex]

That can be any grade.

Therefore:

[tex]C(8,6)*C(11,2)=28*55=1540[/tex]

Where the combination formula is given by:

[tex]C(n,k)=nCk=\frac{n!}{k!(n-k)!}[/tex]

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