Choose President & 2-Person Committee from 8 People - 168 Ways

[caters]

Homework Statement

In how many ways can a president and a 2-person committee be chosen from a group of 8 people (where the order in which we choose the 2 people doesn't matter)? (The president cannot be on the committee.)

Homework Equations

nCr = n!/(r!*(n-r!))

The Attempt at a Solution

8C1(for president) * 7C2(for committee)
=
8*21
=
168 ways

Did I do it right?

 

[mfb]

Correct.

 

[thelema418]

Yes. There are also multiple ways to do this problem. You could have done {}_8 C_3 \times 3 = 168.