A pizza parlor offers four sizes of pizza and 14 different toppings. A customer may choose any number of toppings (or no topping at all). How many different pizzas does this parlor offer?

The number of pizzas offered by a pizza parlor.

Approach:

The number of ways of selecting r objects taken at a time from a total of n objects is given by,

C(n,r)=n!r!(n−r)! ...(1)

The subsets of s elements is given by,

Number of subsets=2s ...(2)

The total number of ways of selecting r objects with s elements taken at a time from a total of n objects is given by,

Number of ways=C(n,r)(2s)

Given:

Number of size of pizza available are 4. Number of toppings available for selecting in a pizza are 14.

Calculation:

Calculate the number of ways of selecting the base size of pizza

Substitute 1 for r and 4 for n in equation (1) to find the number of pizza available in different shapes.