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 effected. 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) The number of different three-number lock combinations is (Type an integer or fraction. Simplify your answer.) (b) The probability that the correct lock combination is guessed on the first try is (Type an integer or fraction. Simplify your answer.)
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 effected. 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) The number of different three-number lock combinations is (Type an integer or fraction. Simplify your answer.) (b) The probability that the correct lock combination is guessed on the first try is (Type an integer or fraction. Simplify your answer.)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.CT: Chapter Test
Problem 3CT: An Internet service provider requires its customer to select a password consisting of four letters...
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Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Transcribed Image Text: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 effected. 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) The number of different three-number lock combinations is
(Type an integer or fraction. Simplify your answer.)
(b) The probability that the correct lock combination is guessed on the first try is
(Type an integer or fraction. Simplify your answer.)
Enter your answer in each of the answer boxes.
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