# Thread: Ice Cream Problem

1. ## Ice Cream Problem

If a company has 50 flavors and 25 different toppings available, how many different combinations are there? Repeating is allowed.

Thanks

2. ## Re: Ice Cream Problem

What have you tried? Do you have any idea?

3. ## Re: Ice Cream Problem

If "repeating is allowed" and there are no other constraints, the is no upper bound to the number of ways.

4. ## Re: Ice Cream Problem

Hello, tabone35!

We need a LOT of clarification . . .

A company has 50 ice cream flavors and 25 toppings available.
How many different combinations are there? .Repeating is allowed.

Are we combining one ice cream flavor with one topping?

What does "repeating" mean?

Could a combination be:
. . (vanilla, vanilla, vanilla, chocolate) + (hot fudge, hot fudge, whipped cream) ?

Sounds like the Spam sketch!

If the term "combination" means:
. . any number of ice cream flavors (up to 50)
. . and any number of toppings (up to 25),
we have an entirely different probem.

There are $2^{50}-1$ combinations of ice cream flavors
. . and $2^{25}$ combinations of toppings.