SOLUTION: In a local high school, from a group of 16 students comprised of 7 singers and 9 actors, a 6-person executive council is selected. How many different executive councils are pos

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Question 1076110: In a local high school, from a group of 16 students comprised of 7 singers and 9 actors, a 6-person executive council is selected.

How many different executive councils are possible if the council must include at least
4 actors?
I tried 7C4 + 12C2
Answer was 3612
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
4 actors it is 9C4
Therefore, there are two singers and that is 7C2
126*21=2646
But it said at least 4 actors
Use 5. That is 9C5=126*7 ways to choose the singer=882
Use 6 actors, which is 9C6=84
2646+882+84=3612