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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 vegitarian and 1 non-vegitarian on the committee?

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

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

d)For one of these cases, determine the number of ways of choosing and distributing the 10 toppings.

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