SOLUTION: An ATM keypad has ten keys. A PIN code is entered by pressing a sequence of four keys. A bank changes the PIN codes to a sequence of six keys. Find the number of PIN codes pos

Algebra ->  Permutations -> SOLUTION: An ATM keypad has ten keys. A PIN code is entered by pressing a sequence of four keys. A bank changes the PIN codes to a sequence of six keys. Find the number of PIN codes pos      Log On


   

Question 1036025: An ATM keypad has ten keys. A PIN code is entered
by pressing a sequence of four keys.
A bank changes the PIN
codes to a sequence of six
keys. Find the number of
PIN codes possible if a key
may be pressed more than
once in a sequence. Discuss the increase in security
by going to a six-key code.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

For a 4-digit code the number of possibilities is 

10 choices for the first digit.
10 choices for the second digit.
10 choices for the third digit.
10 choices for the fourth digit.

That's 104 = 10000 possible 4-digit PINs.

10 choices for the first digit.
10 choices for the second digit.
10 choices for the third digit.
10 choices for the fourth digit.
10 choices for the fifth digit.
10 choices for the sixth digit.


That's 106 = 1000000 possible 4-digit PINs.

For a discussion of increased security of 6 digits over 4, 
go to this website:

https://www.intego.com/mac-security-blog/ios-9-boost-passcode-security/

Edwin