Rugby rules math

Question

Western's rugby team scored 27 points in their last game. All their points came from these three ways of scoring:A try is worth 5 points.

After scoring a try, a team can attempt a conversion, worth 2 points.

A drop goal is worth 3 points.

Question: 

List all the ways they could have scored their 27 points.

Part 2: Explain your strategy for making sure you haven't missed any possibilities.

Answer 1

5 pts 2 pts 3 pts

try, conversion, drop goal

0 0 9

0 3 7

0 6 5

0 9 3

0 12 1

3 0 4

5 1 0

try "tries" as 0, then 1, 2, 3, 4, and 5

increase conversions from 0 to 12 for each

then find drop goals as the residue for the above

4 1