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At Pete's Pizza Palace there are four different toppings you can get on a pizza (all pizzas come with cheese and sauce): Onions, Strawberries, Pepperoni, and Chocolate. How many different pizzas can you order at Pete's? You can have any combination of the toppings you want including no toppings or all four toppings.

 Sep 21, 2019
 #1
avatar+961 
+2

To find the number of toppings, we can use some counting.

0 toppings = 1 way

1 topping = 4 ways

2 toppings = 6 ways

3 toppings = 4 ways

4 toppings = 1 way.

Therefore, you can do it 16 ways. (Chocolate is an interesting topping!)

 

You are very welcome!

:P

 Sep 21, 2019
 #2
avatar+104869 
+2

Number of pizzas with no toppings  = 4C0  =  1

 

Number of pizzas with one topping =  4C1  = 4

 

Number of pizzas with two toppings  =  4C2  =  6

 

Number of pizzas with 3 toppings  =  4C3   = 4

 

Number of pizzaswith all 4 toppings  = 4C4   = 1

 

So...the number of possible pizzas  =  1 + 4 + 6 + 4 + 1  =  16

 

 

cool cool cool

 Sep 21, 2019
 #3
avatar+23317 
+2

At Pete's Pizza Palace there are four different toppings you can get on a pizza

(all pizzas come with cheese and sauce):
Onions, Strawberries, Pepperoni, and Chocolate.
How many different pizzas can you order at Pete's?
You can have any combination of the toppings you want including no toppings or all four toppings.

 

\(\begin{array}{|c|cccc|} \hline \text{binary} & \text{Onions} & \text{Strawberries} & \text{Pepperoni} & \text{Chocolate} \\ \hline 0 & 0 & 0& 0& 0 & \\ \hline 1 & 0 & 0& 0& 1 & \\ \hline 2 & 0 & 0& 1& 0 & \\ \hline 3 & 0 & 0& 1& 1 & \\ \hline 4 & 0 & 1& 0& 0 & \\ \hline 5 & 0 & 1& 0& 1 & \\ \hline 6 & 0 & 1& 1& 0 & \\ \hline 7 & 0 & 1& 1& 1 & \\ \hline 8 & 1 & 0& 0& 0 & \\ \hline 9 & 1 & 0& 0& 1 & \\ \hline 10& 1 & 0& 1& 0 & \\ \hline 11& 1 & 0& 1& 1 & \\ \hline 12& 1 & 1& 0& 0 & \\ \hline 13& 1 & 1& 0& 1 & \\ \hline 14& 1 & 1& 1& 0 & \\ \hline 15& 1 & 1& 1& 1 & \\ \hline \end{array}\)

 

There are 16 different pizzas

 

laugh

 Sep 21, 2019

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