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how many different subsets of $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$ contain at least one element in common with each of the sets $\{2, 4, 6, 8, 10, 12\}$, $\{3, 6, 9, 12\}$ and $\{2, 3, 5, 7, 11\}\,?$

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