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

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. ThusThis is a multivariate hypergeometric distribution count, including the implicit factor $\left(\genfrac{}{}{0ex}{}{2}{0}\right)=1$ for blanks. Dividing by $\left(\genfrac{}{}{0ex}{}{98}{7}\right)$ instead would incorrectly condition on having drawn no blanks.