A certain three three -cylinder combination lock has 65 65 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 three three -number lock combination has been affected. repetitions are allowed, and any of the 65 65 numbers can be used at each step to form the combination. (a) how many different lock combinations are there

Question

Clara Thomas

Mathematics

11 September, 10:09

A certain three three -cylinder combination lock has 65 65 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 three three -number lock combination has been affected. repetitions are allowed, and any of the 65 65 numbers can be used at each step to form the combination. (a) how many different lock combinations are there

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Marshall Graham · Answer 1

Since there are 65 different numbers in each cylinder and any of the 65 numbers can be used at each step to form the combination.

Then, the number of different lock combinations that are possible is given by 65 x 65 x 65 = 274,625.