Number of possibilities ?

[h=1]I run a pizza shop and I want to know how many different combinations of pizza I can do?[/h]
We have 2 Sizes
We have 3 Types of base sauces
5 different types of cheese
20 different toppings
They can only select 1 size and 1 base sauce ( tomato, Bbq or 1/2 & 1/2 mix ), they can select unto 5 different cheese options ( one is to have no cheese ) , they can select upto 20 different toppings, they can select one topping or 19 ( the 20th option is no topping )
I am struggling to work out how many different combination there can be. Can someone help please?

Assuming patrons have to choose a size, sauce, cheese, and topping, your answer will be in the form:

(# of ways to choose sizes) * (# of ways to choose sauces) * (# of ways to choose cheese) * (# of ways to choose toppings)

I'm assuming you mean that there are 19 toppings and you can choose to not have a topping.

Post your work and we can help you further with finding out the specific numbers.

bazzabaker71 said:

I run a pizza shop and I want to know how many different combinations of pizza I can do?
We have 2 Sizes
We have 3 Types of base sauces
5 different types of cheese
20 different toppings
They can only select 1 size and 1 base sauce ( tomato, Bbq or 1/2 & 1/2 mix ), they can select unto 5 different cheese options ( one is to have no cheese ) , they can select upto 20 different toppings, they can select one topping or 19 ( the 20th option is no topping )
I am struggling to work out how many different combination there can be. Can someone help please?

Click to expand...

The parts in red could be read in more than one way. This answer is based on the reading: there are FIVE actual cheeses and nineteen actual toppings with the twentieth being none.
In a set of five objects, there are \(\displaystyle 2^5=32\) possible subsets including the emptyset (no cheese).

It is a bit trickier with toppings due to the way you worded it: there are \(\displaystyle 2^{19}\) possible subsets including the emptyset (no topping).


This gives \(\displaystyle \Large 2\cdot 3\cdot 2^5\cdot 2^{19}\). The last factor depends on exactly what you meant.

This is consistent with the model Dennis posted. But the reading is different.