The number of nonempty subsets of a set with n elements is (see Wikipedia).
I've been challenged to come up with the total possible number of combinations for a given set of ingredients. For the purposes of this challenge, AB == BA. In other words, given ingredients 'A', 'B', and 'C', the possible combinations are as follows:
A, B, C, AB, AC, BC, ABC
BA,CA,CB,ACB,BAC,BCA,CAB, and CBA are not counted because for our purposes order is irrelevant. Also, each item may only be used once. It's been a LONG time since I got out of school, but I can't think of an equation that satisfies this set of rules. Am I missing something obvious? Is there a more complex formula that is required? Any assistance would be greatly appreciated.