# Homework Help: A password with 8 characters, consisting of Upper case/Lower Case &0-9

1. Aug 13, 2014

### laura_a

1. The problem statement, all variables and given/known data

I am a helping out a friend who is studying Maths at uni, not much help really because I did my degree 10 years ago. I am stuck on a question I was hoping for someone help with the working out:

A password consist of 8 characters from Uppercase letters, U, lowercase letters L and Digits 0-9, D.

How many passwords consist of at least one character from U,L & D

I interpreted this question that it would have to inlcude ULD in the password.

Anyway I know there are more cases but I think this is wrong anyway - any suggestions will be appreciated.
2. Relevant equations

3. The attempt at a solution

7 D + 1 U/L = 10^7 x 52 x 8c1
7 U + 1 D/L = 26^7 x 36 x 8c1
7 L + + 1 D/U = 26^7 x 36 x 8c2
6 D + 2U = 10^6 X 26^2 x 8c2
6 D + 2L = 10^6 X 26^2 x 8c2
6 U + 2D = 26^6 x 10^2 x 8c2 x 2(for L)
6 U + 2L = 26^6 x 26^2 x 8c2

Then 1 - (the answer above) is 1.9983 x 10^14

2. Aug 13, 2014

### phinds

Hm ... how about, for example, 4D + 2L + 2U? Does that not meet the criteria? In other words, I think you have specified the MINIMUM amount, not the actual amount.

Also, with your interpretation of one each, I don't see how 6D + 2U, for example, would meet the criteria.

3. Aug 13, 2014

### laura_a

I though that 6D + 2U would suit because then I am taking the answer away from 1 so I actually want the opposite of 6D+2U ?