Question

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

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!