Question: 2014 Winter Midterm - 5
A password consists of 12 or 13 characters, each character being one of the 10 digits $0,1,2,\dots,9$.
A password must contain the digit 7 at least once. How many passwords are there?
(a)
$10^{12} + 10^{13} - 9^{12} - 9^{13}$
(b)
$12^{10} + 13^{10} - 12^{9} - 13^{9}$
(c)
$10^{12} + 10^{13} - 7^{12} - 7^{13}$
(d)
$12^{10} + 13^{10} - 12^{7} - 13^{7}$