1 .
Let $n \geq 2$ be an even integer. A permutation $a_1,a_2,\dots,a_n$ of the set $\{1,2,\dots,n\}$ is
called awesome if $a_2 = 2 \cdot a_1$.
For example, if $n = 6$, then the permutation $3,6,4,1,5,2$ is awesome, whereas the permutation $3,5,4,1,6,2$ is not awesome.
How many awesome permutations of the set $\{1,2,\dots,n\}$ are there?
For example, if $n = 6$, then the permutation $3,6,4,1,5,2$ is awesome, whereas the permutation $3,5,4,1,6,2$ is not awesome.
How many awesome permutations of the set $\{1,2,\dots,n\}$ are there?
(a)
$n \cdot (n-2)!$
(b)
${\frac{n}{2}} \cdot (n-1)!$
(c)
$n \cdot (n-1)!$
(d)
${\frac{n}{2}} \cdot (n-2)!$