a) We have three standard 6-sided dice, colored red, yellow, and green. In how many ways can we roll them to get a sum of 9? The dice are colored so that a red 2, yellow 3, and green 4 is a different roll from red 3, yellow 4, and green 2.
These numbers are small enough so I can just count them
| Green | number left | Y/R | Y/R
| Number of combination |
| 1 | 8 | 2 | 6 | 2 |
| 1 | 3 | 5 | 2 | |
| 1 | 4 | 4 | 1 | |
| 2 | 7 | 1 | 6 | 2 |
| 2 | 5 | 2 | ||
| 3 | 4 | 2 | ||
| 3 | 6 | 1 | 5 | 2 |
| 2 | 4 | 2 | ||
| 3 | 3 | 1 | ||
| 4 | 5 | 1 | 4 | 2 |
| 2 | 3 | 2 | ||
| 5 | 4 | 1 | 3 | 2 |
| 2 | 2 | 1 | ||
| 6 | 3 | 1 | 2 | 2 |
| TOTAL | 25 |
(b) We have 10 standard 6-sided dice, all different colors. In how many ways can we roll them to get a sum of 20?
Yea you can think about this one by thinking of the logic that happened with my first one.
I might think on it later. :)