To open a combination lock, you turn the dial to the right and stop at a number;

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 15 numbers, 0 through 14, determine the number of different combinations possible for the lock.

You have a combination lock. Again, to open it you turn the dial to the right and stop at a first number; then you turn it to the left and stop at a second number. Finally, you turn the dial to the right and stop at a third number. Suppose you remember that the three numbers for your lock are 2, 9, and 5, but you don't remember the order in which the numbers occur. How many sequences of these three numbers are possible?

Explanation / Answer

a.The turning left and right is immaterial here. All it serves to do is to tell you that the order of the numbers matters, but really that was obvious with it being a lock. So you have to spin right, stop at one of eight numbers (15), AND then you turn left and stop at another number, possibly the same one (15), AND then you turn right again and stop at a third number, possibly the same one as before (15).

By the rule of product there are 15³ or 3375 different combinations.

b. number of sequences possible=3!=6

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