Ononot — Let S = \{1, 2, \dots, 10\}. Suppose we want to partition S

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Set Theoryhard

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Let $S = \{1, 2, \dots, 10\}$ . Suppose we want to partition $S$ into three disjoint non-empty sets $A, B, C$ such that the sum of the elements in each set is equal. How many such partitions $\{A, B, C\}$ of $S$ exist?