Question 553009
This seems like it should be easy but I don't know where to begin. 
If Zachary rolls a fair die five times, what is the probability
that the sum of his five rolls is 20?
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Patterns that give sum = 20: 
66611---5!/(3!*2!) = 10 ways
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66521---5!/2! = 60 ways
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65531---5!/2! = 60 ways
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65522---5!/(2!*2!) = 30 ways
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64442---5!/3! = 20 ways
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64433---5!/(2!*2!) = 30 ways
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64415---5!/2! = 60 ways
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etc.

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Add up all the patterns that add up to 20.
Let's say it's "x".
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The total 3 of die patters for the 5 die is 6^5 = 7776
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Ans: P(sum = 20) = x/7776
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Cheers,
Stan H.
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