Question: 2016 Fall Final - 17
Let $X = \{1,2,\dots,100\}$. We choose a uniformly random subset $Y$ of $X$ having size 17. Define the event
- A = "$4 \in Y$ or $7 \in Y$".
(a)
$\frac{2 \cdot {99 \choose 16}}{100 \choose 17}$
(b)
$1 - \frac{{100 \choose 2} \cdot {98 \choose 15}}{100 \choose 17}$
(c)
$1 - \frac{{98}\choose{15}}{{100}\choose{17}}$
(d)
$\frac{2 \cdot {99 \choose 16} - {98 \choose 15}}{100 \choose 17}$