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 seco
nd 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.
<em>Number of different combinations possible:</em> <u>1,728.</u>
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.
<em>To open the combination lock,</em> you:
First number (<em>turn the dial to the right and stop at a number</em>): there are 12 different options for the first number.
Second number (<em>turn the dial to the left and stop at a second number</em>): there are also 12 different options for the second number.
Third number (<em>turn the dial back to the righ and stop at a third number</em>): again, 12 different options for the third number.
<em>Number of different combinations possible</em>: 12 × 12 × 12 = <u>1,728</u>.
