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?

I will assume the "password" may start with a 0

So let's first of all choose the number of passwords
which would be C(2,1) x C(2,1) x C(2,1) x C(2,1) x C(2,1)
= 2^5 = 32

13578 would be in that choice, but not 31578

So we now have to "arrange" each of these 32 numbers
which would give us 32 x 5! = 3840

at a rate of 5 passwords per second it would take
3840/5 or 768 seconds to crack it

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?

There are 2 choices for the first digit, 2 choices for the second digit, 2 choices for the third digit, 2 choices for the fourth digit, and 2 choices for the fifth digit. Therefore, there are a total of 2^5 = 32 possible passwords.

If the robots can enter 5 passwords per second, it will take them 32/5 = 6.4 seconds to go through all the possible passwords. However, this assumes that they will enter the correct password last. In reality, they may enter the correct password earlier or later than that.

To calculate the time it will take for the killer robots to go through all the possible passwords, we need to determine the number of different combinations they could attempt.

In this case, the password is 5 digits long and contains specific options for each digit. We can calculate the number of different combinations by multiplying the options for each digit:

Options for the first digit: 2 (either 0 or 1)
Options for the second digit: 2 (either 2 or 3)
Options for the third digit: 2 (either 4 or 5)
Options for the fourth digit: 2 (either 6 or 7)
Options for the fifth digit: 2 (either 8 or 9)

To find the total number of combinations, we multiply these options together:

2 * 2 * 2 * 2 * 2 = 32

There are a total of 32 different passwords the robots could attempt.

Since the robots can try 5 passwords per second, we can calculate the time it will take by dividing the total number of passwords by the number of passwords attempted per second:

32 / 5 = 6.4 seconds

Therefore, it will take the killer robots approximately 6.4 seconds to go through all the possible passwords.