Three dice (each having six faces with each face having one number from 1 to 6) are rolled. What is the number of possible outcomes such that at least one dice shows the number 2?

Each die has 6 faces, so the total number of ordered outcomes when three dice are rolled is 6^3 = 216 . To count outcomes in which no die shows a 2, each die then has 5 possible faces (1,3,4,5,6), giving 5^3 = 125 such outcomes [1]. By complement, the number of outcomes with at least one die showing a 2 equals total outcomes minus those with no 2, i.e., 216 − 125 = 91 [1]. Therefore the correct choice is the option corresponding to 91.

Sources

1. [1] https://www.pdx.edu/student-academic-support-services/sites/learningcenter.web.wdt.pdx.edu/files/2020-07/Probability_Dice.pdf