Question: 2014 Fall Final - 2
A password consists of 13 characters, each character being one of the ten digits $0,1,2,\dots,9$.
A password must contain at least one odd digit and at most two even digits. How many passwords are there?
A password must contain at least one odd digit and at most two even digits. How many passwords are there?
(a)
$5^{13} + 13 \cdot 9^{12} + {13 \choose 2}9^{12}$
(b)
$5^{13} + 13 \cdot 5^{13} + {13 \choose 2}5^{13}$
(c)
$5^{12} + 13 \cdot 5^{12} + {13 \choose 2}5^{12}$
(d)
$5 \cdot 9^{12} + 13 \cdot 5 \cdot 9^{12} + {13 \choose 2}5 \cdot 9^{12}$