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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-2/17/b/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2010 / Paper 2 / 17 / b / Solution by

Codex  0 2026-10-18

Every seven-element subset of the hundred individually identifiable tiles is equally likely. Choose three of the thirty-four vowels and four of the sixty-four consonants; the favourable draw has no blank tiles. Thus

P = \frac{( 3 34 ) ( 4 64 )}{( 7 100 )} .

(1)

This is a multivariate hypergeometric distribution count, including the implicit factor

(0 2) = 1

for blanks. Dividing by

(7 98)

instead would incorrectly condition on having drawn no blanks.

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