SOLUTION: Luigi's Pizza has a very simple menu. They only sell pizza, and it only comes in one size. They don't have different varieties of crusts or sauces or cheeses. When you order a pizz

Algebra ->  Permutations -> SOLUTION: Luigi's Pizza has a very simple menu. They only sell pizza, and it only comes in one size. They don't have different varieties of crusts or sauces or cheeses. When you order a pizz      Log On


   

Question 1122446: Luigi's Pizza has a very simple menu. They only sell pizza, and it only comes in one size. They don't have different varieties of crusts or sauces or cheeses. When you order a pizza, all you specify is which toppings, if any, you want on it. They offer eight toppings: sausage, pepperoni, mushrooms, onions, green peppers, spinach, pineapple, and anchovies. They do not allow duplicate topping orders; for example, you can't order a pizza with pepperoni and extra pepperoni.
How many different six-topping pizzas are possible at Luigi's Pizza?

How many different six-topping pizzas are possible if mushrooms must be one of the toppings?

Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
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1)  How many different six-topping pizzas are possible at Luigi's Pizza?  


    Answer.  C%5B8%5D%5E6 = %288%2A7%29%2F%281%2A2%29 = 28.


 
2)  How many different six-topping pizzas are possible if mushrooms must be one of the toppings?  
 

    Answer.  C%5B7%5D%5E5 = %287%2A6%29%2F%281%2A2%29 = 21.

Solved.

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It is about combinations.

On Combinations,  see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Combinatorics: Combinations and permutations".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.