ACME Bank requires customers to establish a unique password

ACME Bank requires customers to establish a unique password before utilizing online banking services. If every password must be five digits and can consist of either letters or numbers, how many customers can potentially utilize the online banking service s without repeating passwords

Solution

There are 26 letters and 10 numbers.

Now, if we consider the upper and the lower case of the letters to be different, then the possible number of distinct letters = 26 x 2 = 52.

So, the number of ways in which each place of the password can be filled = 52 + 10 = 62

So, the possible number of distinct passwords = (62)⁵. As each of the 5 places can take any of the 62 values.

Hence, the number of customers that can potentially utilize the online banking service s without repeating passwords = 916132832.

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If we do not consider the upper case and lower case values to be different, then the possible number in which one place can be filled = 26 + 10 = 36.

So, the total number of possible distinct passwords = (36)⁵.

Hence, the number of customers that can potentially utilize the online banking service s without repeating passwords = 60466176.