Solving Pizza Ordering Dilemmas for Student Council

[chemzz]

A 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 leat 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 committee wants as much variety as possible in the toppings. They decide to order each topping exactly once and to have at least one 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.



i'm really confised on how to go about it...so i really don't know how to try it...

 

[HallsofIvy]

Are you sure this isn't a homework problem?!

How many ways are there to choose a vegetarian? How many ways are there to choose a non-vegetarian? How many people are left to choose the third member from?

Do you know the "fundamental law of counting"? If even A can happen in m ways and event B can happen in n ways, independently of A, then A and B can happen together in mn ways. That's the basic rule for all problems like these.

Now, try them yourself and let us see what you do.

 

[lavi]

http://en.allexperts.com/q/Probability-Statistics-2077/probability-18.htm