Question: 2017 Fall Midterm - 16
Let $X = \{1,2,...,20\}$. You choose a uniformly random 7-element subset $Y$ of $X$. Define the
event
- A = "3 is an element of $Y$ or 13 is an element of $Y$".
(a)
$\frac{2 \cdot {20 \choose 6} - {20 \choose 5}}{{20 \choose 7}}$
(b)
$\frac{{19 \choose 6} + {19 \choose 6}}{{20 \choose 7}}$
(c)
$\frac{2 \cdot {19 \choose 7} - {18 \choose 7}}{{20 \choose 7}}$
(d)
$\frac{2 \cdot {19 \choose 6} - {18 \choose 5}}{{20 \choose 7}}$