SOLUTION: If three standard, six-faced dice are rolled, what is the probability that the sum of the three numbers rolled is 9? Express your answer as a common fraction.

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Question 1189301: If three standard, six-faced dice are rolled, what is the probability that the sum of the three numbers rolled is 9? Express your answer as a common fraction.
Answer by ikleyn(52878) About Me  (Show Source):
You can put this solution on YOUR website!
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If three standard, six-faced dice are rolled, what is the probability
that the sum of the three numbers rolled is 9? Express your answer as a common fraction.
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First of all, there are 6*6*6 = 6^3 = 216 possible different outcomes.

So, the entire space of events has 216 elements.


                    Of them


Triple  (6,2,1)  produces  3! = 6 different favorable triples with the sum of 9.

Triple  (5,3,1)  produces  3! = 6 different favorable triples.

Triple  (5,2,2)  produces       3 different favorable triples.

Triple  (4,4,1)  produces       3 different favorable triples.

Triple  (4,3,2)  produces  3! = 6 different favorable triples.

Triple  (3,3,3)  produces       1           favorable triple.


In all, there are  6+6+3+3+6+1 = 25 favorable triples.


The probability under the problem's question is  P = favorable%2Ftotal = 25%2F216.    ANSWER

Solved.