Skynet's Password Scramble

Discrete Mathematics Level 2

Killer robots are trying to take over the world. They know the password to the doomsday weapon is 5 digits long and contains either 0 or 1, and either 2 or 3, and either 4 or 5, and either 6 or 7, and either 8 or 9. If the robots can enter 5 passwords per second, how long (in seconds) will it take them to go through all the possible passwords?

Details and assumptions

The order of the digits matter. The password 12341 is different from the password 43211.

The password 12341 doesn't satisfy the condition, because it doesn't contain either 6 nor 7 (or alternatively because it doesn't contain either 8 or 9).


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