Question

An ice cream shop has 12 flavors of ice cream, 5 types of cones, and 3 toppings. To purchase a dessert, a customer must choose one flavor and one cone, and may choose one topping. (That is, the dessert must include one ice cream flavor, one cone, but not necessarily a topping. A topping is optional.) How many different desserts can be ordered?

A. 20
B. 21
C. 180
D. 240

Answer 1

The ice cream shop offers 240 different dessert combinations when taking into account all flavors, cones, and optional toppings.

Step-by-step explanation:

To calculate how many different desserts can be ordered at an ice cream shop with 12 flavors of ice cream, 5 types of cones, and 3 toppings, where a customer must choose one flavor and one cone, and may choose one topping (optional), we use basic combinatorics. First, for each ice cream flavor (12 options), there is a choice of cone (5 options), making 12 x 5 = 60 basic combinations without toppings. Since a topping is optional, each of these combinations could be without a topping, or with one of the three toppings, giving us 60 x (1 + 3) = 60 x 4 = 240 total dessert combinations (since the 'no topping' option is also a valid choice).