combination lock requires three selections of numbers, each from 1 through 32. 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?
combination lock requires three selections of numbers, each from 1 through 32. 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?
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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A combination lock requires three selections of numbers, each from 1 through 32. 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
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