A certain four -cylinder combination lock has 55 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 four -number lock combination has been affected. repetitions are allowed, and any of the 55 numbers can be used at each step to form the combination. (a) how many different lock combinations are there

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Mathematics

24 December, 10:14

A certain four -cylinder combination lock has 55 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 four -number lock combination has been affected. repetitions are allowed, and any of the 55 numbers can be used at each step to form the combination. (a) how many different lock combinations are there

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Rhett Aguirre · Answer 1

9,150,625.

Step-by-step explanation:

Any one of the 55 numbers can be combined with any one of the 55 in the other cylinders.

So the number of different combinations are 55^4

= 9,150,625.