1 .
Let $n \geq 2$ be an integer. Consider permutations $a_1,a_2,\dots,a_n$ of the set $\{1,2,\dots,n\}$
for which $a_1 < a_2$. How many such permutations are there?
(a)
$2{n \choose 2} \cdot (n-2)!$
(b)
$\frac{n!}{2}$
(c)
$n!$
(d)
None of the above.