Question

To open a combination lock, you turn the dial to the right and stop at a number; then you turn it to the left and stop at a second number. Finally, you turn the dial back to the right and stop at a third number. If you used the correct sequence of numbers, the lock opens. If the dial of the lock contains 8 numbers, 0 through 7, determine the number of different combinations possible for the lock. Note: The same number can be reused consecutively

Answer 1

There are 512 possible combinations for the lock.

Explanation:

This can be modeled as a combination of 8 in 3, meaning we have 8 options to fill 3 dials.

As we can repeat the numbers, we have 8 options for the first number, 8 options for the second number and 8 options for the third number.

This can be written as:

`C=8\cdot 8\cdot 8=8^3=512`

There are 512 possible combinations for the lock.