Question

a new pizza parlor is having a sale as shown below.
sale!
2 topping large pizza
plus your choice of sauce
$7.50
the pizza parlor is offering five different types of meat toppings, seven types of vegetables, and four types of sauce. if two different toppings are on each pizza, how many different types of pizza can a customer make?
a 132
b 528
c 140
d 264
e 3,360

Explanation:

Step1: Calculate total toppings

First, find the total number of topping options. There are 5 meat toppings and 7 vegetable toppings, so total toppings \( n = 5 + 7 = 12 \).

Step2: Calculate combinations of toppings

We need to choose 2 different toppings from 12. The combination formula is \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 12 \), \( k = 2 \). So \( C(12, 2)=\frac{12!}{2!(12 - 2)!}=\frac{12\times11}{2\times1}=66 \).

Step3: Calculate total pizza types

For each combination of toppings, there are 4 sauce options. So total pizza types are \( 66\times4 = 264 \).

Answer:

D. 264