Question

A 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?
B) What is the probability of guessing a lock combination on the first try?

A) 343,000
B) 1/70
C) 70^3
D) 70^2

Answer 1

There are 343,000 different lock combinations, and the probability of guessing a combination on the first try is 1/343,000.

Step-by-step explanation:

A) To find the number of different lock combinations, we need to consider each cylinder separately. Since each cylinder has 70 numbers, there are 70 options for the first number. For the second number, there are also 70 options, and the same goes for the third number. Therefore, the total number of combinations is 70 x 70 x 70 = 343,000.

B) The probability of guessing a lock combination on the first try is 1 out of the total number of combinations, which is 1/343,000 or approximately 0.00000291.