1. ## Multiplication Principle

Each student at a school is given a 6 digit code (like 123876 or 001233)

(b) How many codes read the same forward as backward

I think I understand this one.. For a 6 digit number to be same in forward/reverse, I would have to count the possibilities of the first 3 digits? I'm not sure why this is or if it is even right.

(d) How many codes contain at least one even digit

If each digit can hold 0-9, and there are only 5 even numbers in that interval... would it be 5^6?

(c) How many numbers contain only odd digits?

I know this one is 5^6, but I'm curious if this is the same concept as (d) with different wording?

2. ## Re: Multiplication Principle

b) pick any three digit code, there are 1000 of them, these are the first 3 digits, reverse them for the last three digits

d) easiest to compute the number of codes w/no even digits and subtract it from the number of codes.

# of codes with no even digits is $5^6 = 15625$

# of 6 digit codes is $10^6 = 1000000$

# of 6 digit codes w/at least 1 even digit = $1000000 - 15625 = 984375$

c) is not the same as (d). However, the codes in (d) plus the codes in (c) make up all the possible codes.

3. ## Re: Multiplication Principle

Originally Posted by MrJank
Each student at a school is given a 6 digit code (like 123876 or 001233)
(b) How many codes read the same forward as backward
I think I understand this one.. For a 6 digit number to be same in forward/reverse, I would have to count the possibilities of the first 3 digits? I'm not sure why this is or if it is even right.
(d) How many codes contain at least one even digit
If each digit can hold 0-9, and there are only 5 even numbers in that interval... would it be 5^6?
(c) How many numbers contain only odd digits?
There are $10^6$ possible 6-digits codes.

b) There are $10^3$ 3-digits codes So there are that many 6-digit codes which read either way. WHY? HOW?

Do c) next! odd digits, $\{1,~3,~5,~7,~9\}$ five in all. Thus there $5^6$ codes with only odd digits.

d) Is the answer here $10^6-5^6~?$