Question

An ice cream parlor has 18 different flavors, 5 different kinds of sauce, and 11 toppings. In how many different ways can a dish of three scoops of ice cream can be made if no flavor can be repeated, and only one sauce and one topping will be used? (4 points)

Please show all the work

Answer 1

How many different ways can a dish of three scoops of ice cream if no flavor can be repeated and one sauce and one topping will be used:

Given 18 different flavors

5 different kind of sauce

11 toppings

Solution:

Selecting 3 scoops of ice cream from 18 different flavors where no repetition allowed:

Selecting 3 scoops of ice cream from 18 different flavors where no repetition allowed: 816 combinations.

Now, Adding 1 sauce and 1 toppings to each combination from 5 different kind of sauce and 11 toppings:

(816) * 5 *11 = 44880 combinations

A dish of three scoops of ice cream if no flavor can be repeated and one sauce and one topping is used: 44880 combinations.