Consider your ipad’s security. To unlock the screen suppose you need to enter a four digit pass code. How easy is it to guess this pass code?
Using the standard 10 digit keypad, we first have two questions to consider?
  1. Does the order in which the digits are entered matter?
  2. Can you reuse a digit more than once?
For the ipad, if the order does matter and you cannot reuse digits, the number of possible codes can be determined by considering each digit as a separate event with four such events in succession providing the right code. By successively applying the multiplication principle, you find that the number of possible codes is the number of remaining available digits at each step. Namely, \(10 \times 9 \times 8 \times 7 = 5040.\)
On the other hand, if you were allowed to reuse the digits then the number of possible outcomes would be more since all 10 digits would be available for each event. Namely, \(10 \times 10 \times 10 \times 10 = 10000.\)
Now, consider how this changes if you can use a 4 or 6 digit passcode. Determine the number of possible passcodes.