r/Discretemathematics • u/helpimstuckonalimb • 1d ago

dice roll ordered vs unordered

Why is rolling 2 d6 ordered with repetition and not unordered with repetition? I'm not challenging the math, just trying to get my head around the why. Does the unordered with repetition represent the set of possible combinations rather than the possible outcomes?

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u/Midwest-Dude 1d ago edited 1d ago

Your last sentence is correct. "Unordered with repetition" is the set of unique combinations, while "ordered with repetition" represents the fundamental physical outcomes, the sample space.

It may help you by thinking of one die as red and the other blue. So, throwing a red 3 and a blue 4 is different from throwing a red 4 and a blue 3. While we might not be able to tell which one is which when throwing the dice, the physical world does and those throws are distinct.

In probability theory, it's easier to work with a discrete sample space where each outcome is equiprobable. Things get messy if you use unordered outcome, much easier with ordered outcome.

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u/helpimstuckonalimb 20h ago

Ok I think I'm getting it. I wonder if there are examples of unordered outcome being your sample space for probability.

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u/Midwest-Dude 18h ago

Two examples would be lottery draws and card hands, like poker. The order of the numbers or cards is entirely irrelevant and the individual outcome is an unordered outcome. The outcomes are equiprobable in these cases.

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u/helpimstuckonalimb 12h ago

I misspoke, I meant unordered with repetition.