What is the probability that at least two of the faces match when you roll three fair six-sided dice? Express your answer as a common fraction.

ant101 Feb 20, 2018

#4**0 **

It looks like the above answer is from Mr. BB or one of his students.

**For this question, itâ€™s easier to count the negations, i.e when there are no matches.**

\(\small \text {There are six ways to roll the first die. (6)}\\ \small \text {There are five ways to roll the second die for it NOT to match the first. (5)}\\ \small \text {There are four ways to roll the third die for it NOT to match the first or second. (4) }\\ \small \text {So, there are } 6*5*4 = 120 \text { ways to roll three dice with NO matches. }\\ \small\text {And there are }6^3 \text {ways to roll all combinations. (216) }\\ \large 1- \dfrac {6*5*4}{216} = \dfrac{5}{9} \approx 44.44 \% \)

GA

GingerAle Feb 21, 2018