Question 465514: The Fundamental Counting Principle states that the number of ways in which a series of successive things can occur is found by multiplying the number of ways in which each thing can occur. That is, if first event E1 can occur in M1 different ways and after E1 has occurred, if event E2 can occur M2 different ways, then total number of ways that two events can occur is M1*M2
1.Based on this principle, how many different Social Security numbers are possible?
2.Can you find out how many telephone numbers are possible within any area code?
3.Try following problem using Fundamental Counting Principle.
A typical alarm code is unarmed with the correct sequence of three numbers between 0 and 49 inclusive. If a burglar takes one second to try one sequence of
alarm code, how long (in hours) will take for a burglar to try all possible sequences? Is this alarm code systems deterrent enough to keep burglars away?
Found 2 solutions by Ashlynbyrd, solver91311:
Answer by Ashlynbyrd(1)   (Show Source):
You can put this solution on YOUR website! A typical alarm code is unarmed with the correct sequence of three numbers between 0 and 49 inclusive. If a burglar takes one second to try one sequence of
alarm code, how long (in hours) will take for a burglar to try all possible sequences?
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
50 ways to choose the first number (1 to 49 plus 0), then 50 ways to choose the second number, then 50 ways to chose the third number, so  ways. Once you have calculated the number of ways, divide by 3600 seconds per hour to get the number of hours.
Is it enough of a deterrent? Who knows? How stupid and/or persistent is the burgler in question? How often do you check or use the alarm panel yourself? Did you set an easily guessed combination like 999 or 000 or 123?
John
My calculator said it, I believe it, that settles it
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