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

Guest Jul 27, 2022

#1**0 **

The only possible combinations are

5 5 6

5 6 5

6 5 5

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

Guest Jul 27, 2022

#4**0 **

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 \({2 \times 3 \over 216} = {6 \over 216} = \color{brown}\boxed{1 \over 36}\)

BuilderBoi Jul 27, 2022