If three, standard, 6-faced dice are rolled, what is the probability that the sum of the face up integers is 16?
The only possible combinations are
5 5 6
5 6 5
6 5 5
So the probability is 3/6^3 = 1/72.
+2666 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 \({2 \times 3 \over 216} = {6 \over 216} = \color{brown}\boxed{1 \over 36}\)
