Sum it up!

Algebra Level 5

Let \(T = \{5, 8, 11, 14, \ldots, 47, 50\}\) and let \(S\) be the sum of \(3\) pairwise distinct integers chosen from \(T\). How many distinct possible values are there for \(S\)?

Details and assumptions

3 integers are pairwise distinct if no two of them are equal.

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