Question 388929: Select 3 numbers at random from 1 to 9. What is the probability that the sum of 3 numbers selected is 6. Give answer as a common fraction?
Answer by gwendolyn(128)   (Show Source):
You can put this solution on YOUR website! We can determine the probability by dividing the the number of outcomes which meet the criteria by the total number of possible outcomes (since all the outcomes are equally likely).
There are 9 possible choices for each number, for a total of 9*9*9 possible different outcomes. These could be enumerated, but that would be tedious.
We will determine the number of outcomes which meet the criteria by enumerating them. We can enumerate the results which add up to six pretty quickly. These are all the possible combinations of (4,1,1), (3,2,1) and (2,2,2). Drawing 4,1,1 is different outcome from 1,4,1 and 1,1,4. The different orders represent different outcomes, and therefore need to be counted separately.
4 1 1
3 2 1
3 1 2
2 3 1
2 2 2
2 1 3
1 4 1
1 3 2
1 2 3
1 1 4
So, there are 10 possible combinations that add up to 6 out of a total of 9^3 possible rolls, making the probability:
 = 10/729
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