   Chapter 9.5, Problem 18ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Suppose that you placed the letters in Example 9.5.11 into positions in the following order: first the M. then the I’s, then the S’s, and then the P’s. Show that you would obtain the same answer for the number of distinguishable orderings.

To determine

To prove:

The answer is same for the number of distinguishable orderings for the word MISSISSIPPI.

Explanation

Given information:

Consider various ways of ordering the letters in the word MISSISSIPPI :

IIMSSPISSIP, ISSSPMIIPIS, PIMISSSSIIP, and so on.

Suppose that you placed the letters in MISSISSIPPIinto positions in the following order: first the M, then the I’s, then the S’s, and then the P’s.

Proof:

Since the order in which we select the positions for the same letter doesn’t matter, we should use the definition of a combination.

The word MISSISSIPPI contains 11 letters (positions) of which 1 is an M, 2 are P’s, 4 are I’s and 4 are S’s.

First, we select 1 of the 11 positions for the M, next we select 2 of the remaining 111=10 positions for the P’s, next we select 4 of the remaining 102=8 positions for the I’s and finally we select 4 of the remaining 84=4 positions for the S’s.

LetterM:( 11 1 )=11!1!( 111)!=11!1!10!=11waysLetterP:( 10 2 )=10!2!

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