- #1
srfriggen
- 306
- 5
Homework Statement
How many ways can you roll an 18 from 5 dice? Assume the dice are different colors.
Homework Equations
Factorials
The Attempt at a Solution
I listed combinations of dice that would add to 18 as follows
66411
65511
55521
44442
33336
66312
65412
55431
44433
66222
65313
55224
44451
Since the dice are different colors, then 6, 6, 4, 1, 1 is distinct from 1, 1, 4, 6, 6. The number of orderings of each sum is 5!
So I have, as a solution: 13 x 5! = 1,560
If all the dice were identical then I'd have 460.
I am confused because this site https://wizardofodds.com/gambling/dice/2/ shows that my answer is double what they have.
I think my answer is correct, since my dice are not identical, but am perplexed as to how they got 780 and I get 460 for combinations.