1 .
Consider permutations $a_1,a_2,\dots,a_{10}$ of the set $\{1,2,\dots,10\}$ for which
- $a_1,a_3,a_5,a_7,a_9$ are all odd and
- $a_2,a_4,a_6,a_8,a_{10}$ are all even.
(a)
$2 \cdot (5!)^2$
(b)
$5^5 \cdot 5^5$
(c)
$10!$
(d)
$(5!)^2$