TR-MO-R1 2012 Problem 32

$1, 2, 3, 4, 5, 6, 7, 8, 9, 10$ sayılarının $(a_1, a_2, \dots, a_{10})$ permütasyonlarından kaçı için, $|a_1 - 1| + |a_2 - 2| + \cdots + |a_{10} - 10| = 4$ olur?

a) $60$ b) $52$ c) $50$ d) $44$ e) $36$

Official text Turkish Mathematical Olympiad, first round 2012 official paper, page 9. Quoted with source.

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