The student council wants to form a committee of 3 people to order pizzas for their next meeting. There are 20 members on the student council, 7 of which are vegetarians.

How many different pizza committees can be formed if there must be at least 1 vegetarian and 1 non-vegetarian on the committee?

I assume that means at least one vegetarian and at least one non-vegetarian?

Suppose we choose 1 vegetarian, then the other two must be non-vegetarian.

C(7,1)C(13,2)=546

2 vegetarians and 1 non-vegetarian:

C(7,2)C(13,1)=273

Add them up.