In this problem you will count the number of passwords with certain characterist

Question

In this problem you will count the number of passwords with certain characteristics. The characters in the passwords are all letters or digits. You can assume all letters are lowercase, so there are only 26 letters

a.How many passwords there are with the given restrictions that are six characters long?

b.How many passwords are there that are six characters long that contain at least one digit?

c.How many passwords are there that are six characters long and have have at least one digit and one letter?

Explanation / Answer

a. Since there are six characters in a password and a total of 36 characters and digits, the total number of passwords

= (36+6-1)C6 = 41C6 = 41*40*39*38*37*36/720 = 4496388

b. First we calculate the total number of passwords with no digits.

= (26+6-1)C6 = 31C6 = 31*30*29*28*27*26/720 = 736281

Therefore, the number of passwords with atleast one digit = 4496388 - 736281 = 3760107

c. Total passwords with only digits = (10+6-1)C6 = 15C6 = 15*14*13*12*11*10/720 = 5005

Therefore total passwords with atleast one digit and atleast one letter = 3760107 - 5005 = 3755102

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