 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/18/a/solution

All size-six subsets are equally likely under uniform sampling without replacement. There are

(6 12)

subsets in total, and

(3 6) (3 6)

contain the required three members from each group. Thus the hypergeometric distribution gives

P = \frac{( 3 6 ) ^{2}}{( 6 12 )} = \frac{400}{924} = \frac{100}{231} \approx 0.4329.

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