Pizza Palace Combinations Problem

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cdavison

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Feb 16, 2016
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Please help! I have the following problem I have to solve for my problem solving class and I'm not sure how to do it. I also need to explain the process used to figure it out clearly and completely...

Your friend owns the Pizza Palace restaurant. She is redesigning her menu, and she wants you to help her figure out the maximum number of pizzas she can claim to offer. Customers can choose either traditional crust or gluten free crust, and then they can choose any number of the following toppings: pepperoni, sausage, mushrooms, onion, green pepper, black olives, and anchovies. All pizzas come with cheese. How many different pizza combinations can be made out of the options on Shelby's menu?

Thank you!!
 
cdavison said:
Please help! I have the following problem I have to solve for my problem solving class and I'm not sure how to do it. I also need to explain the process used to figure it out clearly and completely...

Your friend owns the Pizza Palace restaurant. She is redesigning her menu, and she wants you to help her figure out the maximum number of pizzas she can claim to offer. Customers can choose either traditional crust or gluten free crust, and then they can choose any number of the following toppings: pepperoni, sausage, mushrooms, onion, green pepper, black olives, and anchovies. All pizzas come with cheese. How many different pizza combinations can be made out of the options on Shelby's menu?

Thank you!!
Click to expand...

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

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Work so far

So far I tried using Pascal's Triangle, but I'm not sure if I'm doing this properly...

For one crust:

1 topping-7 possibilities [7:1]
2 toppings-21 possibilities [7:2]
3 toppings-35 possibilities [7:3]
4 toppings-35 possibilities [7:4]
5 toppings-21 possibilities [7:5]
6 toppings-7 possibilities [7:6]
7 toppings-1 possibility [7:7]

That would mean there are 127 possibilities per crust, with two possible crusts...254 combinations.
 
cdavison said:
She is redesigning her menu, and she wants you to help her figure out the maximum number of pizzas she can claim to offer. Customers can choose either traditional crust or gluten free crust, and then they can choose any number of the following toppings: pepperoni, sausage, mushrooms, onion, green pepper, black olives, and anchovies. All pizzas come with cheese. How many different pizza combinations can be made out of the options on Shelby's menu?
Click to expand...
Clearly a customer must chose one of two crusts.
He/she can chose anywhere from no toppings to all seven toppings.

If there is a set contains \(\displaystyle n\) elements then there are \(\displaystyle 2^n\) subsets of that set. That includes every subset from the emptyset to the set itself.

The emptyset represents no topping (a cheese piazza); the set itself represents all topping.

Now you read post #2 and follow it. Post your answers to this questions.
Please do reply if you want help in the further help.
 
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