# Combination and Permutation problem

• Jul 8th 2010, 10:54 AM
fabxx
Combination and Permutation problem
I'm really stuck on these problems. I would greatly appreciate it if someone can help me.

A computer hacker is trying to break into a computer system by guessing the system administrator's password. The hacker can try 11 passwords a minute, but if he tries unsuccessfully for more than 14 minutes a day, he will get caught. If he limits his attempts to less time each day, he will not get caught. The hacker knows that the administrator's password is at least 5 and at most 9 characters long, does not contain any character that is not a number, an uppercase letter, or a lowercase letter (no special characters such as spaces, punctuation marks, dollar signs, etc.), and that the first character is a letter. Case matters, and characters can be repeated.

1. How many passwords are there that start with a letter, contain only numbers and upper and lowercase letters, and are at least 5 and at most 9 characters long?

My reasoning: there are 10 numbers (0,1,2,3,4,5,6,7,8,9) and 26 uppercase letters and 26 lowercase letters.

First character has to be a letter so 52 possible outcomes
2nd character can be numbers, or letters (lowercase/uppercase) so 62 possible outcomes
...
I added all the possible numbers of characters together so

(52x62^4)+(52x62^5)+(52x62^6)+(52x62^7)+(52x62^8) =1153981146946451

I have a feeling this is wrong though

2. What fraction of the passwords that start with a letter, contain only numbers and upper and lowercase letters, and are at least 5 and at most 9 characters long can the hacker try in 10 years without getting caught? (Assume that every year lasts 365.25 days.)

He can only hack 11 passwords a minute and no more than 14 mins in a day. I multiplied 11x14 by 362.25 days and then 10 years and got

11x14x362.25x10=562485

To get the fraction, I divided 562485 by the answer i got in question 1

so 562485/1153981146946451 =4.8742997360e-11

Is this correct?

Thank you!