Question

1. An ice cream store has 3 different types of cones for ice cream. They have waffle cones, cup cones (sit down cones) and sugar cones (pointed cones). There are 31 flavors of ice cream and 7 different toppings (chocolate sprinkles, multi-colored sprinkles, nuts, chocolate chips, cookie crumbs, peanut butter chips, M&M’s). a. How many different cones can be made if one item from each category is chosen? b. How many different cones can be made if two scoops of ice cream are allowed on the cone and two toppings are allowed?

Answer 1

3 different types of cones for ice cream. They have waffle cones, cup cones (sit down cones) and sugar cones (pointed cones).

There are 31 flavors of ice cream and 7 different toppings (chocolate sprinkles, multi-colored sprinkles, nuts, chocolate chips, cookie crumbs, peanut butter chips, M&M’s).

a. No. of diff combos = 3*31*7 = 651

b. Ok. So, choose any of the cone in 3 ways

Choose any of 2 toppings in 7C2 = 21 ways

Choose any of the 2 ice cream flavors in 31C2 ways =465 ways

Hence, total no. of ways in which 2 scoops and 2 toppings are allowed: 29295