### Home > CCA2 > Chapter 12 > Lesson 12.1.3 > Problem12-60

12-60.

Another pizza parlor had a super special. The parlor had a rack of small pizzas, each with three or four different toppings. The price was really low because an employee forgot to indicate on the boxes what toppings were on each pizza. Eight toppings were available, and one pizza was made for each of the possible combinations of three or four toppings. Homework Help ✎

1. How many pizzas were on the rack?

Find how many types of pizzas with three toppings can be made.

8C3

Find how many pizzas with four toppings can be made.

8C4

8C3 $+$ 8C4$= 56 + 70 = 126$

2. What was the probability of getting a pizza that had mushrooms on it?

If mushrooms are a known topping, then you choose one fewer topping from only $7$ remaining toppings.

$\frac{_{7}C_{3}+_{7}C_{2}}{126}=\frac{56}{126}=\frac{4}{9}$