Question 6
Four fair, identical dice are rolled. Let $x_i\in\{1,2,\ldots,6\}$ be the result of die $i$, for $i=1,2,3,4$.
(a) How many ordered outcomes $(x_1,x_2,x_3,x_4)$ are possible?
(b) Find the probability that one result equals the sum of the other three.
(c) Find the probability that the four results can be divided into two groups of equal sum.
(a) How many ordered outcomes $(x_1,x_2,x_3,x_4)$ are possible?
(b) Find the probability that one result equals the sum of the other three.
(c) Find the probability that the four results can be divided into two groups of equal sum.