For this problem, assume gwen and harry have 5 types of cones and 9 flavors of ice cream.
(1) in how many different ways can your order one cone and two scoops of ice cream? (as in the book, putting one flavor on top of another is different from putting them the other way around.)
(2) in how many different ways can your order one cone and two scoops of ice cream which are not the same flavor?

Hello!

In this problem you can chose 3 options:

the type of cone, the first flavour, and the second flavour.

a) In how many different ways can your order one cone and two scoops of ice cream?

You have 5 options for cones, 9 options for the first ball of ice cream, and 9 options for the second ball of ice cream (because you can repeat flavour) then the total number of combinations is the product of this 3 numbers, this is:

5*9*9 = 405 combinations

b) Here we cant order the same flavour of ice cream, then:

we still have 5 options for cones, 9 options for the first ball of ice cream, and this time 8 options for the second ball ( because we need to remove the flavour that we picked in the first ball of ice cream) then the number of combinations is:

5*9*8 = 360 combinations.

you already gave the answer

step-by-step explanation: