SOLUTION: At Enzo's Pizza Parlor, there are 7 different toppings, where a customer can order any number of these toppings. If you dine at the said pizza dinner, with how many possible can yo

Algebra ->  Permutations -> SOLUTION: At Enzo's Pizza Parlor, there are 7 different toppings, where a customer can order any number of these toppings. If you dine at the said pizza dinner, with how many possible can yo      Log On


   



Question 1006098: At Enzo's Pizza Parlor, there are 7 different toppings, where a customer can order any number of these toppings. If you dine at the said pizza dinner, with how many possible can you actually order your pizza?
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
There are 2 choices you can make for each topping, they are:

Choice 1: "Yes, I want that topping put on my pizza."
Choice 2: "No, I don't want that topping put on my pizza."

You can make a choice about the 1st topping in 2 ways.
For both those choices, you can make a choice about the 
2nd topping in 2 ways.

That's 2×2 ways to make choices about the first 2 toppings. 

For those 2×2 choices you can make for the first 2 toppings, 
you can make a choice about the 3rd topping in 2 ways.
That's 2×2×2 ways to make choices about the first 3 toppings. 

For those 2×2×2 choices you can make for the first 3 toppings, 
you can make a choice about the 4th topping in 2 ways.
That's 2×2×2×2 ways to make choices about the first 4 toppings.

For those 2×2×2×2 choices you can make for the first 4 toppings, 
you can make a choice about the 5th topping in 2 ways.
That's 2×2×2×2×2 ways to make choices about the first 5 toppings.

For those 2×2×2×2×2 choices you can make for the first 5 toppings, 
you can make a choice about the 6th topping in 2 ways.
That's 2×2×2×2×2×2 ways to make choices about the first 6 toppings.

For those 2×2×2×2×2×2 choices you can make for the first 6 toppings, 
you can make a choice about the 7th topping in 2 ways.
That's 2×2×2×2×2×2×2 ways to make choices about the 7 toppings. 

Answer 2×2×2×2×2×2×2 = 27 = 128 ways to make choices
about your pizza.

However, if you said "no" to all those toppings then all you have is
a pizza crust! :)  So maybe a pizza crust is not considered a pizza,
and so your teacher might say that the answer is only 127 instead of
128.  :)

Edwin