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## 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.