To calculate the 9 most likely numbers to roll with all three dice, you need to work out the possible die combinations for each roll (from 3 to 18).

They are the following:

3 - (1+1+1) Possible Combinations: 1

4 - (1+2+1) Possible Combinations:1

5 - (1+3+1) (1,2,2) Possible Combinations:2

6 - (1,4,1) (1,3,2) (2,2,2) Possible Combinations:3

7 - (1,4,2) (1,3,3) (5,1,1) (3,2,2) Possible Combinations:4

8 - (1,4,3) (1,2,5) (1,1,6) (4,2,2) (3,3,2) Possible Combinations: 5 9 - (6,2,1) (5,3,1) (5,2,2) (4,4,1) (4,3,2) (3,3,3) Possible Combinations:6 10 - (6,3,1) (6,2,2) (5,3,2) (5,4,1) (4,4,2) (4,3,3) Possible Combinations:6 11 - (6,4,1) (6,3,2) (5,5,1) (5,4,2) (5,3,3) (4,4,3) Possible Combinations:6 12 - (6,5,1) (6,4,2) (6,3,3) (5,5,2) (5,4,3) (4,4,4) Possible Combinations:6 13 - (6,6,1) (6,5,2) (6,4,3) (5,5,3) (5,4,4) Possible Combinations:5 14 - (6,4,4) (6,5,3) (5,5,4) (6,6,2) Possible Combinations:4 15- (6,6,3) (6,4,5) (5,5,5) Possible Combinations:3

16- (6,6,4) (6,5,5) Possible Combinations:2

17- (6,6,5) Possible Combinations:1

18- (6,6,6) Possible Combinations:1

This means that there are a total of 56 possible combinations in total. So, to put it in fractions:

3- 1/56

4- 1/56

5- 2/56

6- 3/56

7- 4/56

8- 5/56

9- 6/56

10- 6/56

11- 6/56

12- 6/56

13- 5/56

14- 4/56

15- 3/56

16- 2/56

17- 1/56

18- 1/56

This shows that the numbers 9, 10, 11 and 12 all have a probability of 6/56 (the highest) and 18, 17, 1 and 2 all have a probability of 1/56 (the lowest). So four of the numbers are chosen (9, 10, 11, 12). The numbers with the second highest probability (5/56) are 8 and 13. Those are added to the list. Then, both with 4/56, 7 and 14. And, finally, either 15 or 6, both with 3/56. So, our table should look like this:

91011

12138

14715/6