 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-1/16/b/ii/solution

Choose the first face in six ways, the second in five ways avoiding the first, and the third in four ways avoiding both. Thus

P (D) = \frac{6 \cdot 5 \cdot 4}{216} = \frac{5}{9} .

Each ordered outcome is equally likely in this sample space, so dividing the count by

216

gives the probability.

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