Answer: 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.
