Problem:
Four fair six-sided dice are rolled. What is the probability that at least three of the four dice show the same value?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If exactly three of the four dice show the same number, then there are possible choices for the repeated value and possible choices for the non-repeated value. The non-repeated value may appear on any one of the dice, so there are possible ways for such a result to occur. There are ways for all four dice to show the same value. There are total possible outcomes for the four dice. The probability of the desired result is .
The problems on this page are the property of the MAA's American Mathematics Competitions