SOLUTION: If we roll 4 dice once, what is the chance the sum will be 12?

Question 473709: If we roll 4 dice once, what is the chance the sum will be 12?
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If we roll 4 dice once, what is the chance the sum will be 12?
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Sums range from 4 to 24
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Count the # of ways to get a sum of 12.
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The probability you want is that # divided by 24
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Cheers,
Stan H.
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Answer by Edwin McCravy(20086) (Show Source): You can put this solution on YOUR website!
If we roll 4 dice once, what is the chance the sum will be 12?

The other tutor didn't even start to solve your problem. Counting the number of ways to have sum 12 is NO EASY TASK! And the denominator is not 24 at all. It's 6⁴. There are these 11 sets of ways disregrading order that the 4 dice can have sum 12. However the dice are different so we must rearrange each of these in all possible distinguishable arrangements: 1. 1 1 4 6 <-- 4!/2! = 12 distinguishable arrangements 2. 1 1 5 5 <-- 4!/(2!2!) = 6 distinguishable arrangements 3. 1 2 3 6 <-- 4! = 24 distinguishable arrangements 4. 1 2 4 5 <-- 4! = 24 distinguishable arrangements 5. 1 3 3 5 <-- 4!/2! = 12 distinguishable arrangements 6. 1 3 4 4 <-- 4!/2! = 12 distinguishable arrangements 7. 2 2 2 6 <-- 4!/3! = 4 distinguishable arrangements 8. 2 2 3 5 <-- 4!/2! = 12 distinguishable arrangements 9. 2 2 4 4 <-- 4!/(2!2!) = 6 distinguishable arrangements 10. 2 3 3 4 <-- 4!/2! = 12 distinguishable arrangements 11. 3 3 3 3 <-- 4!/4! = 1 distinguishable arrangement The numerator of the desired probability is 12+6+24+24+12+12+4+12+6+12+1 = 125 The denominator is 6⁴ since each die can land 6 ways: So the answer is = Edwin

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