To cancel an electronic alarm, a 5-digit code number must be entered into the code box. Assuming that digits may be repeated, how many codes are possible?
Think of this question from perspective of the person who sets the code.
When he picks the first of the 5 digits, how many choices does he have? Exactly 10 choices!
When he picks the second of his 5 digits, he can again choose from 10 options.
For digits 3, 4 and 5 he also has 10 choices.
So he has 10*10*10*10*10 choices or 10^5.
To contract: if repetition is not allowed, there are
For the first digit he can choose any number 0-9.
For the second digit he can choose any number 0-9 EXCEPT the number he chose for the first digit, so he has 9 options.
And so on.