Prove that A is a subset of B if and only if B complement is a subset of A complement.
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If the letters are considered distinct, then the number of permutations is 
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If we count either C as the same character, then we would be double-counting - to correct this, we would simply divided by the number of ways we can choose C from the available characters, or
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If we count either C as the same character, then we would be double-counting - to correct this, we would simply divided by the number of ways we can choose C from the available characters, or