subcommittee must have no more than 3 grade 12 students

Grr Im still having trouble with these type of questions:

A student fundraising committee has 14 members, including 7 members from grade 12. In how many ways can a 4-membr subcommittee fo the commencement awards be formed if,

the subcommittee must have no more than 3 grade 12 students?

I did 7C3* 7C1 ..I don't know how to carry on, or if that's even right.

thanks.

You may want to count each case. That is, 0, 1, 2, 3 seniors are chosen.

\(\displaystyle \L\\\underbrace{C(7,0)}_{\text{no seniors}}\overbrace{C(7,4)}^{\text{4 non-seniors}}+\underbrace{C(7,1)}_{\text{1 senior}}\overbrace{C(7,3)}^{\text{3 non-seniors}}+\underbrace{C(7,2)}_{\text{2 seniors}}\overbrace{C(7,2)}^{\text{2 non-seniors}}+\underbrace{C(7,3)}_{\text{3 seniors}}\overbrace{C(7,1)}^{\text{1 non-senior}}\)

Another thing you could do is count up the ways to select 4 seniors and subtract from the total number of ways 4 people are chosen from 14.

\(\displaystyle \L\\C(14,4)-C(7,4)C(7,0)\)

Do you get the same answer for both methods. If you do, that may be a good sign.

yep same answers, thanks. Yea I tihnk ill do these type of questions the 2nd way, I get that way more better