Question 1043930
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How many subsets of {3, 7, 11, 12} have 11 as a member? (Calculate
this without listing the subsets.) 
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It is the same as to ask  

    How many subsets are in the set {3, 7, 12}?


The answer is {{{2^3}}} = 8.


The number of subset of the finite set containing N elements is {{{2^N}}}
(including the set itself as a subset and the empty subset).


See the lesson <A HREF=https://www.algebra.com/algebra/homework/word/misc/How-many-subsets-are-there-in-a-given-finite-set-of-n-elements.lesson>How many subsets are there in a given finite set of n elements?</A> in this site.
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