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

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- Solution 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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