# probability problem

• Aug 16th 2008, 10:30 AM
sevenlovesyou
probability problem
I cant remember how to solve these.

A computer password consists of eight letters. How many passwords are possible? Assume there is no difference between lower-case and upper-case letters.

• Aug 16th 2008, 11:08 AM
Chris L T521
Quote:

Originally Posted by sevenlovesyou
I cant remember how to solve these.

A computer password consists of eight letters. How many passwords are possible? Assume there is no difference between lower-case and upper-case letters.

What we are dealing with here is a permutation.

Recall that $\displaystyle _nP_r=\frac{n!}{(n-r)!}$ where $\displaystyle r\leq n$.

Since the password can contain only letters, and we are to assume that there is no difference between lower and upper case we must let $\displaystyle n=26$ [if there was a difference between upper and lower case, $\displaystyle n=52$]. Since the password can only be 8 letters long, let $\displaystyle r=8$.

So we see that we now have $\displaystyle _{26}P_8=\frac{26!}{18!}$

Can you take it from here?

--Chris
• Aug 16th 2008, 12:45 PM
Plato
It has been my experience that passwords allow for repetitions, such as “youuttta”.
In that case the answer would be $\displaystyle {26}^8$.