The dial on a combination lock shows the integers 0 through 39. Turning the dial to...
The dial on a combination lock shows the integers 0 through 39. Turning the dial to three specific numbers (in order) opens the lock.
a) How many different locks can a manufacturer produce before they have to reuse combinations, if numbers cannot be repeated in a combination (i.e., 25-17-25 is not allowed)?
How many different locks can a manufacturer produce before they have to reuse the combination if numbers can be repeated in a combination?
Homework Answers
(a). There can be 40 possible first numbers in a combination, but for each of them, the condition against repeating means there are only 39 possible second number, and 38 choices for the third. Therefore, the number of different combinations is,
(b). If we can repeat numbers, then we can use any of the 40 numbers for each stage, therefore, the number of different combinations is,
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