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

bigmac Dec 9, 2019

#1**+1 **

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.

Melody Dec 10, 2019