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with recursion, in a loop, you take one item from the list and past the remaining items to the next level. Continue on down until only one left.

Do you know what a recursive method call is? That is a common way to solve this problem. That is what would be used when the input can be any number of letters.
If your problem will always have 5...

What techniques has your instructor talked about? Did he give you any hints or clues on how to solve this?

Is this a "make all possible combinations" project?
For example. given 1,2,3 : 123,132,213,231,312,321