 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-1/1/solution

(1 + x)^{8} = \sum_{k = 0}^{8} (k 8) x^{k}

. The required binomial coefficients are therefore

[x^{4}] (1 + x)^{8} = (4 8) = 70, [x^{5}] (1 + x)^{8} = (5 8) = 56.

Here

[x^{k}]

denotes the coefficient of

x^{k}

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