Discrete math: using product and sum rule

Question

How many ways can we get a total of 11on a die roll involving three distinguishable six sided dice? By this, we mean we keep track of which die rolls which number. A 3 on a red die, 3 on a blue die and 5 on a green die would count as one possibility while a 3 on a red die, 5 on a blue die and 3 on a green die would count as another. What if the dice are not distinguishable?

Answer 1

6^3=216 possible outcomes from 111 to 666

outcomes 3 to 18

1 way to get 3

3 ways to get 4

6 for 5

9 for 6

15 for 7

20 for 8

25 for 9

27 for 10

27 for 11 ***********

25 for 12

20 for 13

15 ror 14

9 for 15

6 for 16

3 ways to get 17

1 way to get 18

1.4,6

1,5,5

16,4

only 155 and 146, if indistinguishable

2,3,6

2,4,5

2,5,4

2,6,3

only 236 and 245

3,2,6

3,3,5

3,4,4

3,5,3

3,6,2

only 335 and 344

4,1,6

4,2,5

4,3,4

4,4,3

4,5,2

4,6,1

515

524

533

542

551

614

623

632

641

3+4+5+6+5+4=27

only 2+2+2= 6 if indistinguishable