Choosing a Divisibile Sum

A set of four distinct numbers are chosen from the set \(\{1,2,3 \ldots 9, 10, 11\}\). How many ways can this set of \(4\) numbers be chosen such that the sum is divisible by \(3\)?

Details and assumptions

Choosing the numbers \( \{ 1, 2, 3, 6 \} \) is the same as choosing the numbers \( \{ 6, 3, 2, 1 \} \).

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