 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/iv/solution

The sample space outcomes with qualifying sums have totals three, four and five. Their ordered patterns are

(1, 1, 1)

, the three permutations of

(1, 1, 2)

, and the three permutations each of

(1, 1, 3)

and

(1, 2, 2)

. Thus there are

1 + 3 + 3 + 3 = 10

qualifying outcomes:

P (F) = \frac{10}{216} = \frac{5}{108} .

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