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Answer :
Final answer:
It will take approximately 59.5 hours to test all possible combinations of the lock.
Explanation:
To calculate the number of possible combinations, we need to determine the total number of options and the number of choices. In this case, the numbers on the lock's dial range from 0 to 35, so there are 36 options for each number in the combination.
Since there are three numbers in the combination and each number is different, we can use the formula for combinations to calculate the total number of possible combinations:
nCr = n! / (r!(n-r)!)
Plugging in the values, we have:
36C3 = 36! / (3!(36-3)!)
Simplifying the expression:
36C3 = 36! / (3!33!)
Using factorials, we can further simplify:
36C3 = (36 * 35 * 34) / (3 * 2 * 1)
Calculating the expression:
36C3 = 7140
So, there are 7140 possible combinations.
Now, to calculate the time it will take to test all possible combinations, we multiply the number of combinations by the time it takes to test each combination:
7140 combinations * 30 seconds per combination = 214,200 seconds
Converting seconds to hours:
214,200 seconds / 3600 seconds per hour = 59.5 hours
Therefore, it will take approximately 59.5 hours to test all possible combinations.
Learn more about calculating the time required to test all possible combinations of a lock here:
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Final answer:
It will take approximately 59.5 hours to test all possible combinations of the lock.
Explanation:
To calculate the number of possible combinations, we need to determine the total number of options and the number of choices. In this case, the numbers on the lock's dial range from 0 to 35, so there are 36 options for each number in the combination.
Since there are three numbers in the combination and each number is different, we can use the formula for combinations to calculate the total number of possible combinations:
nCr = n! / (r!(n-r)!)
Plugging in the values, we have:
36C3 = 36! / (3!(36-3)!)
Simplifying the expression:
36C3 = 36! / (3!33!)
Using factorials, we can further simplify:
36C3 = (36 * 35 * 34) / (3 * 2 * 1)
Calculating the expression:
36C3 = 7140
So, there are 7140 possible combinations.
Now, to calculate the time it will take to test all possible combinations, we multiply the number of combinations by the time it takes to test each combination:
7140 combinations * 30 seconds per combination = 214,200 seconds
Converting seconds to hours:
214,200 seconds / 3600 seconds per hour = 59.5 hours
Therefore, it will take approximately 59.5 hours to test all possible combinations.
Learn more about calculating the time required to test all possible combinations of a lock here:
https://brainly.com/question/28209576
#SPJ14
