Suppose an ice cream store offers 34 flavors of ice cream cones in sizes small, medium, and large. If four toppings are available to put on a cone, and a cone can be bought without a topping, how many different selections of ice cream are available if each cone has one flavor and one or no toppings?
A)136,306,272
B)1,156
C)196,520
D)5,780
E)39,304

Question

Suppose an ice cream store offers 34 flavors of ice cream cones in sizes small, medium, and large. If four toppings are available to put on a cone, and a cone can be bought without a topping, how many different selections of ice cream are available if each cone has one flavor and one or no toppings? ​
A)136,306,272
B)1,156
C)196,520
D)5,780
E)39,304

Quizplus · Accepted Answer

There are three choices for sizes of cones, and each cone has 34 flavor options plus the option to have no flavor. Therefore, there are:

3 (cone size choices) x 35 (flavor and no flavor choices) = 105 options for just the cone and flavor.

For each of those 105 options, there are 5 choices for the toppings: no topping or any combination of the 4 toppings available.

Therefore, for each of the 105 cone and flavor options, there are 5 choices for toppings, giving us:

105 (cone and flavor options) x 5 (topping options) = 525 options for cone, flavor, and toppings.

Thus, the total number of different selections of ice cream available is:

105 (cone and flavor options) x 5 (topping options) = 525 options

Answer: C) 196,520.

Suppose an Ice Cream Store Offers 34 Flavors of Ice