Kenneth S. answered • 07/13/17

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The number of ways to have frozen yogurt combinations is 1 up to 18 flavors!

That 18C1 + 18C2 + 18C3 + ... + 18C17 + 18 C18 which (if you know the binomial theorem you'll understand this) equals exactly 2

That 18C1 + 18C2 + 18C3 + ... + 18C17 + 18 C18 which (if you know the binomial theorem you'll understand this) equals exactly 2

^{18}- 1. Indeed a large number.Now # of toppings, if any combination from NONE up to all 80 is possible, that equals exactly 2

^{80}.The product of these two numbers is the answer desired.

*Of course, it is not economically feasibble, so this is the theoretical maximum...very big, but a lot less than infinity, which I cannot begin to describe!*