Question

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

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.