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Question: 2017 Winter Final - 1

Author: Michiel Smid

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.

How many such permutations are there?

(a)

$5^5 \cdot 5^5$

(b)

$2 \cdot (5!)^2$

(c)

$(5!)^2$

(d)

$10!$