Discussion

Three dice, each having six faces numbered 1 to 6, are rolled. What is the number of possible outcomes in which at least one die shows the number 2?

Answer: C

"At least one" is easiest through the complement.

\[ \text{total outcomes} = 6^{3} = 216 \]

\[ \text{no die shows 2} = 5^{3} = 125 \]

\[ 216 - 125 = 91 \]

Counting exactly one, exactly two and exactly three 2's gives \( 75 + 15 + 1 = 91 \) as well, for considerably more work.

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