How many different combinations are possible, if order doesn't matter?

Question

Baskin Robins offers 31 different ice cream flavors. Let's suppose they have 10 different toppings as well.

You device to have a bowl of ice cream with 3 different scoops of ice cream and 2 different toppings.

Answer 1

This question is deceptive! I assume that each scoop  the customer wants is a different flavor of ice cream and that each topping is different.

In light of the above, there are 31x30x29 combinations for flavors, and 10x9 toppings The number of combinations becomes 31x30x29x10x9.

However, it is also possible that the customer wants to have all three scoops to be the same flavor of ice cream or both toppings to be the same. Perhaps he wants two scoops of ice cream to be the same. In this case, the number of combinations will be different.

31x31x31 x10x10

I hope this helps!

Bruce from Grovetown Georgia