Question from Perms and Combs unit

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Homework Help Overview

The discussion revolves around a combinatorial problem involving the arrangement of letters in the word "ELEMENTS," specifically focusing on the alternating pattern of vowels and consonants in five-letter "words."

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to solve the problem by considering two cases based on whether a vowel or consonant starts the sequence. They express confusion regarding the discrepancy between their calculated total and the provided answer.

Discussion Status

Participants are actively engaging with the problem, questioning the treatment of identical letters and discussing the implications of these repetitions on the calculations. Some guidance has been offered regarding the need to account for repeated letters, but no consensus has been reached on the final answer.

Contextual Notes

Participants are considering the implications of identical letters in the arrangement, particularly the two E's in "ELEMENTS," which may affect the total count of unique arrangements.

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Homework Statement


Given the letters of the word ELEMENTS, how many 5 letter "words" can be found in which vowels and consonants alternate


Homework Equations





The Attempt at a Solution


I see the need to use Cases here because the pattern can either go:

v c v c v

or

c v c v c

So I did:

Case 1 : vowel starts 3 5 2 4 1 = 120
Case 2: consonant starts 5 3 4 2 3 = 360

Add them up to get 480, however the answer says 80. What went wrong? Or was that a typo mistake?
 
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Is there any difference between the first and last E?
 
Don't think so.
 
So how many different ways are there to arrange the vowels?
 
Nevermind, I found out what I did wrong, I forgot to divide each case by 3! for the repetitive E's.
 
What do you mean "nevermind", that was what Nate was pointing out all along.
 

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