Combinations: need step-by-step solutions for 'combo' probs

I'd appreciate it if someone could give me a step by step solution for the problem below. I've septn over 2 hours on it!! I'm freaking out someone PLZ help me! You can send me the solution to [e-mail address deleted for security] Thx!!!

The student council is ordering pizza for their next meeting. There are 20 council members, 7 of whom are vegetarians. A committe of 3 will order 6 pizzas with up to 3 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 committee wants as much variety as possible in the toppings. They decide to order each toppings exactly once and to have at least 1 topping on each pizza. Describe the different cases possible when distibuting the toppings in this way.

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

mandy813 said:

I'd appreciate it if someone could give me a step by step solution for the problem below.

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If you've spent two hours on this, reviewing the worked examples in your textbook and in your class notes (and possibly additionally from online lessons) and are still unable to even begin, then I'm afraid you need much more help than we can here provide. :shock:

The volunteers can help students work through specific exercises, but this assistance requires that the student have at least a basic grasp of the underlying material. Unfortunately, it is not reasonably feasible to attempt to provide the hours of instruction necessary to provide this foundational underpinning. And obviously one more worked example isn't going to do the job, when all those other worked examples completely failed. Sorry!

Please seriously consider hiring a qualified local tutor and setting aside an hour or two a day for concentrated private study. By working with you face-to-face, your tutor can review your text, your class notes, and the course handouts, and figure out how far back you need to go to get to material with which you are comfortable. Then your tutor can re-teach the missing concepts, terms, and techniques, and help you get caught up with your class. With some hard work and a little luck, you could be back on schedule in only a few weeks! :idea:

My best wishes to you in your studies!

Eliz.

The student council is ordering pizza for their next meeting. There are 20 council members, 7 of whom are vegetarians. A committe of 3 will order 6 pizzas with up to 3 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.

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I will help get you started.

We are choosing pizza committees. It is made up of 3 people chosen from 20. We have 13 non-vegetarians and 7 vegetarians.

There is 2 ways we can have 'at least' one vegetarian and 'at least' one non-vegetarian. Assuming I am interpreting the problem correctly.

N=non-vegetarian. V=vegetarian.

NNV, VVN

Order does not matter, so we either have 2 V and 1 N or 2 N and 1 V.
For the number of ways to choose 2 non-vegetarians and 1 vegetarians. \(\displaystyle C(13,2)C(7,1)\)

The other case, 2 vegetarians and 1 non-vegetarian is \(\displaystyle C(13,1)C(7,2)\)

Add them: \(\displaystyle C(13,2)C(7,1)+C(13,1)C(7,2)\)