Question

A computer password consists of eight characters.a. How many different passwords are possible if each character may be any lowercase letter or digit?b. How many different passwords are possible if all characters are lower case letters?c. What is the probability of generating a password with all lowercase letters, if a password consists of eight characters and each character may be a lowercase letter or digit?

Answer 1

Answer: Hello there!

We know that the password consists of eight characters:

a) Lower case letters and digits, in any order:

we have a total of 10 digits, and 26 letters, which adds to a total of 36 total possibilities in each of the 8 characters for the password.

then the total number of combinations is:

36^8 = 2.821x10^12

b) Now we only have lower case letters:

Then we have 26 options for each character; now we have:

26^8 = 2.088x10^11 possible combinations.

c) now we want to see the probability of randomly generating a password with only lowercase letters if the password also allows having digits.

this is calculated as the number of combinations for only letters, divided by the number of combinations for letters and digits, which are the numbers of combinations that we obtained in the incises a and b:

p = (2.088x10^11)/(2.821x10^12) = (2.088)/(28.21) = 0.074

wich expressed in percent form is: 0.074*(100%) = 7.4%