I'm working on an assignment and I'm not sure if I'm doing it properly so I figured I'd ask and make sure.
The question is, a university gives each student a 6 digit code for a student number.
a) How many codes are there?
$10 * 9 * 8 * 7 * 6 * 5 = 151,200$, I assumed that each code must be unique
b) How many codes read the same forward as backward?
$10 * 9 * 8 = 720$, If the code is supposed to read the same way forward as backwards then the first digit you'd have 10 choices, meaning the last would only have 1 choice? Then 9 in the second, 1 option in second to last..., if the codes were not unique then would it be $10^3$?
c) How many codes contain only odd digits?
Since there are 5 odd digits between 0-9, $5^6 = 15,625$ number of odd digit codes?
d) How many codes contain at least one even digit?
Not sure about how to do this one.