Question

A computer password consists of six characters.a. How many different passwords are possible if each character may be any lowercase letter or digit, and at least one character must be a digit? Please enter your result in scientific notation, making sure the answer in the left box is between 1 and 10.b. A computer system requires that passwords contain at least one digit. If six characters are generated at random, and each is equally likely to be any of the 26 letters or 10 digits, what is the probability that a valid password will be generated?

Answer 1

Answer:

a) $6.04661760*10^8$

b) 0.27778

Step-by-step explanation:

a)

There are 26 lowercase letters and 10 digits.  

The character that must be a digit can be generated in 10 different ways and the others, in 26+10=36 different ways.

Since the password is 6 characters long, by the Fundamental Rule of Counting there are

10*36*36*36*36*36 = 604,661,760

In scientific notation this number can be expressed as

$6.04661760*10^8$

b)

By the Fundamental Rule of Counting, there would be  

$36^6$

different combinations of 6 characters, but only the number computed in a) are valid combinations, so the probability of generating a valid password is

$\displaystyle\frac{10*36^5}{36^6}=\displaystyle\frac{10}{36}=0.27778$