Probability

Question

 

A large company must chose between two types of passwords to log on to a computer. The first type is a four-letter password using any of the 26 letters of the alphabet, without repetition of letters. The second type is a six-digit password using the digits 0 through 9, with repetition of digits allowed.

Determine the number of possible four-letter passwords.

Determine the number of possible six-digit passwords.

The company has 500,000 employees and needs a different password for each employee. State which type of password the company should choose. Explain your answer.

Answer 1

4-LETTER PASSWORDS

1st letter choice, 26 possibilities; 2nd letter choice, 25 poss; 3rd choice, 24; 4th choice, 23.

26×25×24×23=358,800 total possible passwords. Not enough to cover 500,000.

6-DIGIT PASSCODES

Passcodes start at 000000 and end at 999999, a total of 1,000,000 different passcodes. Easily enough to cover 500,000 employees.

Therefore the 6-digit passcodes cover 500,000 employees and should be used. Having a surplus would allow for employees to leave while others join the company, using unique passcodes, until all existing employees have left and new ones replace them (one complete turnover of staff). After this, the password/passcode system would need to be revised.