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Suppose the 5 letters are A, B, C, D and E.
The letter A can either be in the combination or not: 2 options for A.
With each of these options, B can either be in the combination or not: 2 options for B - making 2*2 options so far.
With each of the options so far, C can either be in the combination or not: 2 options for C - making 2*2*2 options so far.
and so on.
So for 5 letters there are 25 = 32 combinations. However, one of these is the combination that excludes each of the 5 letters - ie the null combination. Excluding the null combination gives the final answer of 31 combinations.
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