Question #338234

What is the number of subsets of a set with n elements, containing a given element (when element becomes fixed, part of every subset)?



1
Expert's answer
2022-05-09T09:51:07-0400

The problem is equivalent to finding a number of subsets of a set with n1n-1 elements. Namely, we take a set without the fixed element(a subset that contains n1n-1 elements) and construct all possible subsets of this set. Then, we add this fixed element to every constructed subset. It remains to solve the following task: find a number of subsets of the set that contains n1n-1 elements. We use the multiplication principle of combinatorics. For any element of the set there are two options: it belongs to the subset or not. We receive: 2n12^{n-1} subsets.

Answer: in case we fix an element of the set and consider all subsets that contain this element, we receive 2n12^{n-1} different subsets.


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