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Three molecules of type A, three of type B, three of type

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 40E Chapter 2

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 40E

Three molecules of type ?A, ?three of type ?B, ?three of type ?C, ?and three of type ?D are to be linked together to form a chain molecule. One such chain molecule is ABCDABCDABCD, ?and another is ?BCDDAAABDBCC. a. How many such chain molecules are there? [?Hint: ?If the three ?A?’s were distinguishable from one another—?A?1, ?A?2, ?A?3—and the ?B?’s, ?C?’s, and ?D?’s were also, how many molecules would there be? How is this number reduced when the subscripts are removed from the ?A?’s?] b. ?Suppose a chain molecule of the type described is randomly selected. What is the probability that all three molecules of each type end up next to one another (such as in ? BBAAADDDCCC) ? ?

Step-by-Step Solution:

Answer Step 1 of 2 There are 12 components in the chain then it can be arranged in 12! Ways The chain is composed of 4 groups of 3 identical models,there are 3! ways each The number of chain molecule= 12! =369600 (3!)

Step 2 of 2

Chapter 2, Problem 40E is Solved
Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

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Three molecules of type A, three of type B, three of type

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