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The number under the question = the number of all non-empty sub-sets of the set of 5 elements.
Answer. In = 32-1 = 31 way.
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The solution uses well known fact that the total number of subsets of a given set of N elements is , including the empty subset and improper subset.
See the lesson
- How many subsets are there in a given finite set of n elements?
in this site.