150 Followers Question

We group the numbers into three groups. The first group contains the numbers which are 1 mod 3, this group contains 5 numbers. The second group contains the numbers which are 2 mod 3, this group contains 4 numbers. The third group contains numbers which are divisible by 3, this group contains 4 numbers. To get a sum that is 0 modulo 3, the numbers can be (1,2,0), (0,0,0), (1,1,1) or (2,2,2). The numbers in the brackets represent the modulo 3 of each individual number and the order does not matter. Thus, the answer is simply $5\cdot4\cdot4+2\left(\begin{array}{c}4\\ 3\end{array}\right)+\left(\begin{array}{c}5\\ 3\end{array}\right)=98$