What is the number of subsets of a set with n elements, containing a given element (when element becomes fixed, part of every subset)?
The problem is equivalent to finding a number of subsets of a set with elements. Namely, we take a set without the fixed element(a subset that contains 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 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: subsets.
Answer: in case we fix an element of the set and consider all subsets that contain this element, we receive different subsets.
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