Certain three -cylinder combination lock has 70 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 -number lock combination has been affected. repetitions are allowed, and any of the 70 numbers can be used at each step to form the combination. (a) how many different lock combinations are there

Question

Karma Krueger

Mathematics

24 January, 04:08

Certain three -cylinder combination lock has 70 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 -number lock combination has been affected. repetitions are allowed, and any of the 70 numbers can be used at each step to form the combination. (a) how many different lock combinations are there

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Rowan Hays · Answer 1

The lock has 3 different cylinders that can take up to 70 possible numbers. The possible combination of each cylinder would be 70!

The order of cylinder would be important because the password on 1st cylinder can't be used on cylinder 2. The calculation would be:

possible lock combination = 1st cylinder possible combination * 2nd cylinder possible combination * 3rd cylinder possible combination

possible lock combination = 70!*70!*70!