Set a={1,2,3,4,5,6} two numbers from set a are selected at random without replacement and their sum recorded how many different sums are possible

The minimum sum is 3 and the maximum is 11. So there are 9 different possible sums.
There are 30 ways to get these 9 different sums.
The table below shows all outcomes.

1 2 3 4 5 6
———————————-
1 | X 3 4 5 6 7
2 | 3 X 5 6 7 8
3 | 4 5 X 7 8 9
4 | 5 6 7 X 9 10
5 | 6 7 8 9 X 11
6 | 7 8 9 10 11 X

The point (5, 10) will work for the rule y=x+5.y= 10 x= 510=5+510=10therefore the ordered pair (5, 10) works for the rule