A combination lock requires three selections of numbers, each from 1 through 37. Suppose the lock is constructed in such a way that no number may be used twice in a row, but the same number may occur both first and third. For example, 20 13 20 would be acceptable, but 20 20 13 would not. How many different combinations are possible? To answer this question, note that some combinations will consist of three different numbers, whereas in others the first and third numbers can be the same.
A combination lock requires three selections of numbers, each from 1 through 37. Suppose the lock is constructed in such a way that no number may be used twice in a row, but the same number may occur both first and third. For example, 20 13 20 would be acceptable, but 20 20 13 would not. How many different combinations are possible? To answer this question, note that some combinations will consist of three different numbers, whereas in others the first and third numbers can be the same.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help me with these two questions!
![A combination lock requires three selections of numbers, each from 1 through 37. Suppose the lock is constructed in such a way that no number may be used twice in a row, but the same number may occur both first and third. For example, 20 13 20 would be acceptable, but 20 20 13 would not. How many different combinations are possible?
To answer this question, note that some combinations will consist of three different numbers, whereas in others the first and third numbers can be the same.
The total number of combinations is [ ] .](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc751bb16-77f1-4244-9ee9-db954bbe7814%2F2dfe47f4-1968-4da0-830c-17870d3dc891%2Fsa3r42m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A combination lock requires three selections of numbers, each from 1 through 37. Suppose the lock is constructed in such a way that no number may be used twice in a row, but the same number may occur both first and third. For example, 20 13 20 would be acceptable, but 20 20 13 would not. How many different combinations are possible?
To answer this question, note that some combinations will consist of three different numbers, whereas in others the first and third numbers can be the same.
The total number of combinations is [ ] .
![(a) How many strings of five hexadecimal digits do not have any repeated digits?
[______]
(b) How many strings of five hexadecimal digits have at least one repeated digit?
[______]
(c) What is the probability that a randomly chosen string of five hexadecimal digits has at least one repeated digit? (Round your answer to the nearest tenth of a percent.)
[______] %](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc751bb16-77f1-4244-9ee9-db954bbe7814%2F2dfe47f4-1968-4da0-830c-17870d3dc891%2Fdxlnn9v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) How many strings of five hexadecimal digits do not have any repeated digits?
[______]
(b) How many strings of five hexadecimal digits have at least one repeated digit?
[______]
(c) What is the probability that a randomly chosen string of five hexadecimal digits has at least one repeated digit? (Round your answer to the nearest tenth of a percent.)
[______] %
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