In a set, as it is usually defined, elements can't be repeated. "Mathematics" has 8 distinct letters, so your set would have 8 letters. The number of possible subsets (this includes the empty set, and the set itself) is two to the power 8.
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In a set, repetition of elements is not regarded as a difference. That being the case, "mathematics" has 8 distinct letters and so there will be 2^8 = 256 subsets (including the null set).
The empty set has only one subset: itself. It has no proper subsets.
The word mathematics has 11 letters; 2 are m, a, t. The number of distinguishable permutations is 11!/(2!2!2!) = 39916800/8 = 4989600.
A set with n elements has 2n subsets. The number of proper subsets is one less, since 2n includes the set itself.
It depends on the set x. If set x is of cardinality n (it has n elements) then it has 2n subsets.
There are 6 such subsets of B.