For additional security, each customer creates a 5-digit PIN (personal identification number). The table at the right shows the 10 most commonly chosen PINs. The table suggests that more than 1/3 (33.33%) of the PINs can be guessed using one of these 10 PINs.

a) How many 5-digit PINs are possible if digits can be repeated? Assume only numbers can be contained in the PIN.

b) You want to enhance security by restricting PINs so that they do not repeat any digits. How many possible PINs would there be?

c) If you were in charge of security, would you decide to restrict PINs so that no digits can be repeated? Think about your answers in (a) and (b) and also consider the table.

 

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Rank 1 2345678 9 10 PIN 12345 11111 55555 00000 54321 13579 77777 22222 12321 99999 Percent 22.80% 4.48% 1.77% 1.26% 1.20% 1.11% 0.62% 0.45% 0.41% 0.40% Rank 1 2345678 9 10 PIN 12345 11111 55555 00000 54321 13579 77777 22222 12321 99999 Percent 22.80% 4.48% 1.77% 1.26% 1.20% 1.11% 0.62% 0.45% 0.41% 0.40%