# How to make 4608 combinations with these choices? (Probability, permutations/combinations)

This problem has been giving me a lot of trouble...

Freeze King claims to offer 4,608 different ice cream cups. A customer can choose from 3 sizes, 4 flavors; a waffle cone, sugar cone, or cup; and any combination of their toppings. How many toppings must Freeze King offer in order to match its claim?

I start out with 3*4*3 because there are 3 sizes, 4 flavors, and 3 cones. But you can pick more than one topping... I'm thinking you would use combinations and have to add them together to equal 128 but I'm not sure where to proceed from there. Is my thinking correct, and how would I proceed from here?

• Out of curiosity, where did the number $96$ come from? I think you accidentally calculated $\frac{4608}{3\cdot 4\cdot 4}$ instead of $\frac{4608}{3\cdot 4\cdot 3}$ – JMoravitz May 26 '15 at 1:30
• That's exactly how I got 96. My apologies, I just edited the OP. – yousefk May 26 '15 at 1:33

Further hint: $4608 = 2^9\cdot 3^2$ so $\frac{4608}{3\cdot 4\cdot 3} = 128 = 2^7$