Question 989959: Number of subsets for {e, m, e, r, a, l, d}
Answer by ikleyn(52867)   (Show Source):
You can put this solution on YOUR website! .
When the set of elements is presented by the list of its elements, it is assumed and supposed that the list contains different elements and no one element is repeated twice.
In your list this agreement is violated, because there are two identical symbols "e". What do they represent? Different elements? Same element?
So, in my view, it is incorrect to use the list like this one as the definition of the set of elements.
In any case, it is a bad style to disturb the young students' brains with such provocations. Sorry.
From the other side, for any finite set of N elements the number of all its subsets is  (including the empty subset).
If the number of elements in the set is 7, then the number of all its subsets is  .
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