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sum of outcomes of three dice (Posted on 2009-11-20) Difficulty: 2 of 5
What is the probability that the sum of outcomes of three dice thrown together is 9?

See The Solution Submitted by Vishal Gupta    
Rating: 3.0000 (1 votes)

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Three Blind Dice | Comment 1 of 4

There are 6^3 = 216 possible outcomes from all three dice.

For those whose sum is 9, there are five groups of possibilities in numeric order:  [1 2 6], [1 3 5], [2 3 4], [1 4 4], and [3 3 3].  The first three groups have distinct values and each have 3! = 6 permutations.  [1 4 4] has a repeating 4 and therfore has only 3 permutations ([1 4 4], [4 1 4], and [4 4 1]).  And [3 3 3] has the same value and therefore has only 1 permutation.  So the number of outcomes that sum to 9 = 3x6 + 3 + 1 = 22, and the probability for this = 22/216 = 11/108.


  Posted by Jim Keneipp on 2009-11-20 13:42:04
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