.
It is the same as to ask
How many subsets of the set A B D E F contain the letter B
(letter C is just EXCLUDED from the set . . . )
Since the new set contains 5 elements, the number of its subsets is = 32,
including the empty subset and the improper subset.
Therefore, the answer to the original question is: 32 subsets, including the empty subset.
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See the lesson
- How many subsets are there in a given finite set of n elements?
in this site.