Question: 2017 Winter Final - 15
Let $n \geq 5$ be an integer. Consider a uniformly random permutation $a_1a_2 \dots a_n$ of the set
$\{1,2,\dots,n\}$. Define the events
- A = "$a_1 = 1$",
- B = "$a_n = 5$".
(a)
None of the above.
(b)
${\frac{2}{n}} - {\frac{1}{n^{2}}}$
(c)
${\frac{1}{n}} - {\frac{1}{n(n-1)}}$
(d)
${\frac{2}{n}} - {\frac{1}{n(n-1)}}$