Question: 2018 Winter Final - 17
Let $n \geq 1$ be an integer.
Consider a uniformly random permutation of the set $\{1,2,3,\dots,2n\}$. Define the event
- A = "both the first element and the last element in the permutation are even integers".
(a)
$\frac{n}{2(2n-1)}$
(b)
$\frac{2(2n-1)}{n-1}$
(c)
$\frac{n-1}{4n}$
(d)
$\frac{n-1}{2(2n-1)}$