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# Combinatorics

Let $$S= \{1,2,.....,n\}$$ and let $$T$$ be the set of all ordered triples of subsets $$S$$, say $$(A_{1}, A_{2}, A_{3})$$, such that $$A_{1} \cup A_{2} \cup A_{3} = S$$. Find the cardinality of $$T$$ in terms of $$n$$. (For example, if $$S = \{1,2,3\}$$ and $$A_{1} = \{1, 2\}, A_{2} = \{2, 3\}, A_{3} = \{3\}$$ then one of the elements of T is ($$\{1, 2\}, \{2, 3\}, \{3\})$$. )

Note by Dhrubajyoti Ghosh
2 weeks, 1 day ago