Practice By Tag: Permutations and Binomial Coefficients

Question: 2019 Winter Midterm - 7

1 . Consider 17-element subsets of the set $\{1,2,3,\dots,45\}$.
How many such subsets have the property that the largest element in the subset is equal to 30?

(a)

${30 \choose 17}$

(b)

${29 \choose 17}$

(c)

${30 \choose 16}$

(d)

${{29}\choose{16}}$