Question

A password consists of four different letters of the alphabet. How many different possible passwords are there?

Answer 1

`(1)/(233974)` (1 out of 233974 chance of correctly guessing the password)

Explanation:

First Part (letter in the password):

There are 26 letters in the alphabet, and there is only one letter in the password. So for that part, you have
`(1)/(26)` chance in finding the letter in the password.

Second Part (4 digit number in the password):

For the next part, the problem says that it’s a four digit number. So, out of all the numbers there are, what place value has four digits? It would be the thousands. That means from 1,000 to 9,999 (not including 10,000 too because that’s 5 digits) is the range of all the possible 4 digit numbers. So, how many numbers are in the range of 1,000 through 9,999? Well, all you do is subtract 1,000 from 9,999 (can be written as 9,999 - 1,000) and that equals 8,999. This means that there are 8,999 possible 4 digit numbers that can be guessed in the password. So that means you will have a 1 out of 8,999 chance in finding the 4 digit number in the password. This can be written as
`(1)/(8999)`.

Final Part (solving it):

Finally, you need to multiply the two chances together (the chance in finding the letter times the change of finding the 4 digit number). This can be written as
`(1)/(26)` ×
`(1)/(8999)`, which equals .

Answer:
`(1)/(233974)` (1 out of 233974 chance of correctly guessing the password)

I hope you understand and that this helps with your question! :)

Answer 2

26 letter in alphabet

several scenarios
1. can repeat and only lowercase
26^4 or 456976 ways

2. can repeat and lower and uppercase
26^4*2^4 or 7311616 ways

3. cannot repeat and only lowercase
26*25*24*23 or 358800 ways

4. cannot repeat and lowercase and uppercase
26*25*24*23*2^4 or 5740800 ways