# Ice Cream Problem

• Oct 13th 2011, 10:59 AM
tabone35
Ice Cream Problem
If a company has 50 flavors and 25 different toppings available, how many different combinations are there? Repeating is allowed.

Thanks :)
• Oct 13th 2011, 11:09 AM
Siron
Re: Ice Cream Problem
What have you tried? Do you have any idea?
• Oct 13th 2011, 12:07 PM
HallsofIvy
Re: Ice Cream Problem
If "repeating is allowed" and there are no other constraints, the is no upper bound to the number of ways.
• Oct 13th 2011, 01:01 PM
Soroban
Re: Ice Cream Problem
Hello, tabone35!

We need a LOT of clarification . . .

Quote:

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