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Rolling to score (Posted on 2010-11-15) Difficulty: 4 of 5
We roll five standard dice (sides numbered 1 to 6) and write down the sum of the top three i.e. of the 3 highest values.
What is the probability to get 15 ?

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.3333 (3 votes)

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Perhaps.... (comment) | Comment 1 of 17

I find this ambiguous.  What if the dice thrown are 41465? The "three highest values" are 4,5,6, and the total of the four dice with those three values is 19.  The total on the three highest dice (not counting more than three) would be 15.

If one sorts the dice from low to high (11111 to 66666) there are 252 unique combinations, of which 31 total 15 for the three dice with the highest values.  This might give 31/252 as the probability (c. 0.123)  but this seems unsatisfactory since the 252 combinations do not occur with the same probability.  I'll just post this to see how others interpret the quest.

  Posted by ed bottemiller on 2010-11-15 13:58:52
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