a computer system requires all users to log on using a 6 character password. if each character can be either a digit from 0 to 9 or a letter of the alphabet, what is the number of possible passwords. please show formula used

there are 10 digits and 26 letters, so there are 36 possible characters for each password character.

so, the total is 36^6 = 2176782336

To calculate the number of possible passwords, we need to know the total number of options for each character and the total number of characters in the password.

In this case, each character can be one of 10 digits (0-9) or one of 26 letters (a-z or A-Z) for a total of 36 options per character. The password length is given as 6 characters.

To find the total number of possible passwords, we can use the formula for permutations. In permutations, the order matters and repetition is not allowed.

The formula for permutations is:

P(n, r) = n! / (n - r)!

Where:
- n is the total number of options for each character
- r is the number of characters in the password

Applying this formula to our case, we have:
n = 36 (total options per character)
r = 6 (number of characters in the password)

P(36, 6) = 36! / (36 - 6)!

Calculating this using the factorial notation:

P(36, 6) = 36! / 30!

Now, we just need to calculate these factorials.

36! = 36 × 35 × 34 × 33 × 32 × 31 × 30!
30! = factorial(30)

By substituting these values into the formula and calculating the result, we can find the number of possible passwords.