CPM Homework Help : A2C Problem 10-154

Another pizza parlor is having a super special. They have a rack of small pizzas, each with three or four different toppings. The price is really low because they forgot to indicate on the boxes what toppings were on each pizza. They had eight toppings available, and they made one pizza for each of the possible combinations of three or four toppings. Homework Help ✎
1. How many pizzas are on the rack?
2. What is the probability of getting a pizza that has mushrooms on it?

Step 1(a):

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

₈C₃

Step 2(a):

Find how many pizzas with four toppings can be made.

₈C₄

Answer 3(a):

₈C₃ + ₈C₄ = 56 + 70 = 126

Hint (b):

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

Answer (b):

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