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Find the number of arrangements of the letters DESCARTES if no two vowels are together.

 Dec 9, 2019
 #1
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Find the number of arrangements of the letters DESCARTES if no two vowels are together.

 

DCRTSS       There are  6!/2! = 360 ways to arange the consonents  

AEE              There are 3 ways to arrange the vowels

 

|*| *| *| *| *| *|   

The stars are the 6 consonants

The 7 bars are possible positons for the 3 vowels.  

So I think that there are   7C3 = 35 place combinatons for the vowels.

 

So the number of arrangements  that I get is  360*3*35 =  37800.

 

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There are never guarantees with prob questions.

I think this is correct but I am open to polite questions or criticisms.

 Dec 10, 2019
edited by Melody  Dec 10, 2019
 #2
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If you intereract with me, and do it politely, you are much more likely to get my help into the future

 Dec 10, 2019

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