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 12 numbers, 0 through 11, determine the number of different combinations possible for the lock. Note: The same number can be reused consecutively.

Answer 1

1728

Step-by-step explanation:

There are 12 numbers that can be used for the first number; 12 for the second number; and 12 for the third number. This means there are a total of

12(12)(12) = 1728 combinations.

Answer 2

• Number of different combinations possible: 1,728.

Step-by-step explanation:

The fundamental principle of counting establises tha if there are A ways to perform an action, B way to perform a second independent action, and C ways of performin a third independent action, then the number of ways to perform the three actions is equal to the product A × B × C.

To open the combination lock, you:

• First number (turn the dial to the right and stop at a number): there are 12 different options for the first number.

• Second number (turn the dial to the left and stop at a second number): there are also 12 different options for the second number.

• Third number (turn the dial back to the righ and stop at a third number): again, 12 different options for the third number.

Number of different combinations possible: 12 × 12 × 12 = 1,728.