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5. Alarm Code Combinations; A security alarm system is activated and deactivated by correctly entering the appropriate three-digit numerical code in the proper sequence on a digital panel. A. Compute the total number of possible code combinations if no digit may be used twice. B. Computer the total number of possible code combinations if digits may be used more than once.

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Answer:

A. 720 combinations

B. 1,000 combinations

Step-by-step explanation:

There are 10 possible numeric digits (from 0 to 9).

A. If  no digit may be used twice, there 10 possibilities for the first digit, 9 for the second, and 8 for the third:

[tex]A = 10*9*8\\A=720\ combinations[/tex]

There are 720 possible combinations

B. If digits may be repeated, there are 10 possibilities for each entry:

[tex]B=10*10*10\\B=1,000\ combinations[/tex]

There are 1,000 possible combinations.