Question: 2016 Fall Final - 13
Let $V$ be a set consisting of 12 even integers and 8 odd integers. We choose a uniformly random
subset $W$ of $V$ having size 7. Define the event
- A = "exactly 4 of the elements of $W$ are even".
(a)
$\frac{{20 \choose 4}{16 \choose 3}}{20 \choose 7}$
(b)
$\frac{{12 \choose 4}{8 \choose 3}}{20 \choose 7}$
(c)
$\frac{{20 \choose 3}{17 \choose 4}}{20 \choose 7}$
(d)
$\frac{{12 \choose 4}+{8 \choose 3}}{20 \choose 7}$