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Combination Locks A combination lock has 50 numbers on it.
Chapter 5, Problem 43E(choose chapter or problem)
Problem 43E
Combination Locks A combination lock has 50 numbers on it. To open it, you turn counterclockwise to a number, then rotate clockwise to a second number, and then counterclockwise to the third number. Repetitions are allowed.
(a) How many different lock combinations are there?
(b) What is the probability of guessing a lock combination on the first try?
Questions & Answers
QUESTION:
Problem 43E
Combination Locks A combination lock has 50 numbers on it. To open it, you turn counterclockwise to a number, then rotate clockwise to a second number, and then counterclockwise to the third number. Repetitions are allowed.
(a) How many different lock combinations are there?
(b) What is the probability of guessing a lock combination on the first try?
ANSWER:
Solution:
Step 1 of 2:
Given that a combination lock has 50 numbers on it.
a). Here we have to find how many different lock combinations are there.
Each three numbers have 50 possible outcomes.
Then the number of all combinations are
Therefore, there are 125000 lock combinations.