Question 1134551: 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 12 numbers, 0 through 11, determine the number of different combinations possible for the lock. NOTE: the same number can be reused consecutively.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! there are 12 possibilities for the first turn.
there are 12 possibilities for the second turn.
there are 12 possibilities for the third and final turn.
the total possible numbers for the combination are 12 * 12 * 12 = 1728
to see how this works, assume only 2 numbers are possible for each turn.
let the numbers be 0 and 1.
you have 2 possibilities for the first turn and two possibilities for the second turn and two possibilities for the third and final turn.
total possibilities are 2 * 2 * 2 = 8.
those possibilities are:
000
001
010
011
100
101
110
111
|
|
|
