Choosing a Divisibile Sum

Probability Level 4

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 $\{ 6, 3, 2, 1 \}$ .