Question

1. An ice cream shop has 25 different flavors of ice cream. For each of the following, indicate whether it is a problem

that involves permutations, combinations, or neither.
a. What is the number of different 3-scoop ice cream cones that are possible if all three scoops are different
flavors, and a cone with vanilla, strawberry, and chocolate is different from a cone with vanilla, chocolate, and
strawberry?
b. What is the number of different 3-scoop ice cream cones that are possible if all three scoops are different
flavors, and a cone with vanilla, strawberry, and chocolate is considered the same as a cone with vanilla,
chocolate, and strawberry?
c. What is the number of different ice cream cones if all three scoops could be the same, and the order of the
flavors is important?

Answer 1

Explanation:

Given that an ice cream shop has 25 different flavors of ice cream.

a) the number of different 3-scoop ice cream cones that are possible if all three scoops are different

=25P3 (since order matters as shapes or colours would be different so different order will give different type)

= 13800

b) the number of different 3-scoop ice cream cones that are possible if all three scoops are different

=25C3 (since order does not matter here)

=2300

c) the number of different ice cream cones if all three scoops could be the same, and the order of the

flavors is important

= when all three sceeps couldbe the same we can say that these are with replacement. Neither permutation nor combination

Each scoop can be any one of the 25

no of ways
`= 25^3=15625`