Unit Key Question - Probability Pizza :)

**The student council is ordering pizza for their next meeting. There are 20 council members, 7 of whom are vegetarian. A committee of 3 will order 6 pizzas from a pizza shop that has a special price for large pizzas with up to three toppings. The shop offers 10 different toppings.**

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

b) In how many ways could the committee choose up to 3 toppings for a pizza?

c) The commitee wants as much variety as possible in the toppings. They decide to order each topping exactly once and to have at least 1 topping on each pizza. Describe the different cases possible when distributing the toppings in this way.

any help for any of these questions would be great.

THANKS!