A certain threethree-cylinder combination lock has 6060 numbers on it. To open it, you turn to a number on the first cylinder

Question

3 years ago

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A certain threethree-cylinder combination lock has 6060 numbers on it. To open it, you turn to a number on the first cylinder

, then to a second number on the second cylinder, and then to a third number on the third cylinder and so on until a threethree-number lock combination has been effected. Repetitions are allowed, and any of the 6060 numbers can be used at each step to form the combination. (a) How many different lock combinations are there? (b) What is the probability of guessing a lock combination on the first try?

Mathematics