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.

1. How many pizzas were on the rack?

   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$= 56 + 70 = 126$

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

   Hint (b):

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

   Answer (b):

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