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?

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- Nov 18th 2008, 02:41 PMJoker37Permutations
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?

- Nov 18th 2008, 04:33 PMrobeuler
There are ten digits: 0, 1, 2,...8, 9

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

10*9*8*7*6 choices.

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.