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In the video "How many ways are there to reorder the word MISSISSIPPI?" by Dr. Trefor Bazett, Dr. Bazett computes the number of reorderings as follows. First he considers the number of places to put all the "S"s, then all the "I"s, then the two "Ps", and finally the "M". The resulting expression is 0000. Yes, math profs make mistakes too... 4 Part A Find the mistake in Dr. Bazett's solution. Describe what the error is and write down the correct solution! (1) Part B Perform the same analysis, but start by placing the "M", then the two "P"s, then the four "I"s, and then the four "S"s. You should get an

In the video "How many ways are there to reorder the word MISSISSIPPI?" by Dr. Trefor Bazett, Dr. Bazett computes the number of reorderings as follows. First he considers the number of places to put all the "S"s, then all the "I"s, then the two "Ps", and finally the "M". The resulting expression is 0000. Yes, math profs make mistakes too... 4 Part A Find the mistake in Dr. Bazett's solution. Describe what the error is and write down the correct solution! (1) Part B Perform the same analysis, but start by placing the "M", then the two "P"s, then the four "I"s, and then the four "S"s. You should get an

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please help me with Problem 2

Problem 2 In the video "How many ways are there to reorder the word MISSISSIPPI?" by Dr. Trefor Bazett, Dr. Bazett computes the number of reorderings as follows. First he considers the number of places to put all the "S"s, then all the "I"s, then the two "Ps", and finally the "M". The resulting expression is (1)() Yes, math profs make mistakes too... 2 Part A Find the mistake in Dr. Bazett's solution. Describe what the error is and write down the correct solution! Part B Perform the same analysis, but start by placing the "M", then the two "P"s, then the four "I"s, and then the four "S"s. You should get an expression that is similar to your corrected answer in Part A, including some of the same numbers, but in different places. Part C Using the formula for (1), write a calculation to show that your answer in Part A agrees with (is the same number as) Dr. Bazett's solution in Equation 1. Part D The method of combinatorial proof is used to show that two expressions are equal by demonstrating that they are different ways of counting the same thing. Use a combinatorial proof to show that, for any integers n, k, and j such that k + j≤n, (1) (3) (" *) = ('?) (^z ^) . j k Note: it is possible to do this with algebra, but please don't! The combinatorial proof is simpler and nicer. Hint: consider the number of ways to reorder a word of length n containing only three kinds of distinct letters.
Transcribed Image Text:Problem 2 In the video "How many ways are there to reorder the word MISSISSIPPI?" by Dr. Trefor Bazett, Dr. Bazett computes the number of reorderings as follows. First he considers the number of places to put all the "S"s, then all the "I"s, then the two "Ps", and finally the "M". The resulting expression is (1)() Yes, math profs make mistakes too... 2 Part A Find the mistake in Dr. Bazett's solution. Describe what the error is and write down the correct solution! Part B Perform the same analysis, but start by placing the "M", then the two "P"s, then the four "I"s, and then the four "S"s. You should get an expression that is similar to your corrected answer in Part A, including some of the same numbers, but in different places. Part C Using the formula for (1), write a calculation to show that your answer in Part A agrees with (is the same number as) Dr. Bazett's solution in Equation 1. Part D The method of combinatorial proof is used to show that two expressions are equal by demonstrating that they are different ways of counting the same thing. Use a combinatorial proof to show that, for any integers n, k, and j such that k + j≤n, (1) (3) (" *) = ('?) (^z ^) . j k Note: it is possible to do this with algebra, but please don't! The combinatorial proof is simpler and nicer. Hint: consider the number of ways to reorder a word of length n containing only three kinds of distinct letters.
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