[psmith]

How do you calculate the number of unique variations if you have 30 possible items to choose from and you can pick 1 to 30 of them?

[Kermit1941]

How do you calculate the number of unique variations if you have 30 possible items to choose from and you can pick 1 to 30 of them?

It sounds like you are asking for the number of non-empty subsets.

Build up to the answer by considering a smaller number of items.

For 1 item, the answer is 1.
For 2 items, the answer is 3,
{a,b} --> {a},{b},{a,b}
For 3 items, the answer is 2 * 3 + 1 = 7
for 4 items, the answer is 2 * 7 + 1 = 15

etc