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Question: 2014 Fall Final - 1

Author: Michiel Smid
A password consists of 13 characters, each character being one of the ten digits $0,1,2,\dots,9$.
A password must contain exactly one odd digit. How many passwords are there?
(a)
$13 \cdot 5^{13}$
(b)
$13 \cdot 9^{12}$
(c)
$13 \cdot 5^{12}$
(d)
$13 \cdot 5 \cdot 9^{12}$