Question

23. Calculate the probability of getting exactly two sixes and one five when rolling five dice. Do this in two different ways, as follows. (a) First calculate the probability that two of the five dice land sixes, and then multiply this by the probability that one of the remaining three lands a five. (note: The remaining three dice have only five ways in which they can land.) (b) Next calculate the probability that one of the five dice lands a five, and then multiply this by the probability that two of the remaining four dice land a six. (c) Are the two results the same? (If not, you have made a mistake.)

Answer 1

(c) So the two answers are same.