If we are using an 4-character password that contains only lowercase English alphabetic characters (26 different characters), how many *more* possible passwords are there if we use a 5-character password (still only lowercase English alphabetic characters?

11,424,400 possible passwords

Explanation:

Since all characters are letters and only lowercase

we have 26∧4 = 456,976 possibilities

For a 5-character password which is still lower case sensitive.

we have 26∧5 = 11,881,376 possibilities

Many more possible passwords = (11881376-456976)

= 11,424,400 possible passwords

If we are using a 4-character password that contains only lowercase alphabets and repetition of these alphabets are allowed then the possible passwords are:      

26 * 26 * 26 * 26 = 26 ^ 4 = 456976

If we are using a 4-character password that contains only lowercase alphabets and repetition of these alphabets are not allowed then the possible passwords are:

n! / (n - r )! = 26! / (26 - 4)! = 358,800

Explanation:

If we are using a 5-character password that contains only lowercase alphabets and repetition of these alphabets are allowed then the possible passwords are:

26 * 26 * 26 * 26 * 26 = 26 ^ 5 = 11881376

If we are using a 5-character password that contains only lowercase alphabets and repetition of these alphabets are not allowed then the possible passwords are:

n! / (n - r )! = 26! / (26 - 5)! = 7893600

how many *more* possible passwords are there if we use a 5-character password:

Possible passwords when we use 5 character passwords - Possible passwords when we use 4 character passwords.

11881376 - 456976 = 11424400