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If three, standard, 6-faced dice are rolled, what is the probability that the sum of the face up integers is 16?

 Jul 27, 2022
 #1
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The only possible combinations are

5 5 6

5 6 5

6 5 5

 

So the probability is 3/6^3 = 1/72.

 Jul 27, 2022
 #2
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What about the case where we get 4, 6, 6 :)

 Jul 27, 2022
 #3
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Did it say the dice are distinguishable? Do we have to consider that?

 Jul 27, 2022
 #4
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There are \(6^3 = 216\) ways to roll the dice

 

There are only 2 ways to get 16:  \((5, 5, 6)\)\((4, 6, 6)\)

 

In both cases, there are \(3! \div 2! = 3\) ways to order them

 

Thus, the probability is \({2 \times 3 \over 216} = {6 \over 216} = \color{brown}\boxed{1 \over 36}\)

 Jul 27, 2022
 #5
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Good method. I think that is correct. :)

 Jul 27, 2022

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