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adell [148]
3 years ago
7

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.
Mathematics
2 answers:
Alex3 years ago
6 0

Answer:

  • <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>.

Tomtit [17]3 years ago
4 0

Answer:

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.

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