Question Part Points Submissions Used To open a combination

Question Part Points Submissions Used 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 7 numbers, 0 through 6, determine the number of different combinations possible for the lock.

Solution

firsw we can choose any of 0 to 6 number in 6 ways, because you are at 0th position.

then maximum you can reach 6th position and in 2nd turn you can back again to 0 by six moves

in 3rd trial maximum you can choose 5th position

hence the total combinations is 6*6*5=180