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## #1 2018-06-09 17:51:30

Amartyanil
Member
From: Universe
Registered: 2013-05-27
Posts: 65

### Letter-arranging

Hi;

Can anyone please provide a detailed solution for this problem?

All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other

Is there any program for solving this? If yes, please provide the code.

"Every place is the center of the universe. And every moment is the most important moment. And everything is the meaning of life." ~ Dan Harmon

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## #2 2018-06-09 19:38:49

bob bundy
Registered: 2010-06-20
Posts: 8,354

### Re: Letter-arranging

hi Amartyanil

First you could calculate the number of arrangements where there is no restriction.

Then imagine EA locked together as a single 'letter' and calculate how many ways you can arrange these five letters.  Do a similar thing with AE etc*.  Then subtract.

Bob

*You'll need to take care to avoid repeats caused by all three vowels together.

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #3 Yesterday 05:25:24

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,856
Website

### Re: Letter-arranging

Is there any program for solving this? If yes, please provide the code.

bobbym used to be a pro at doing these with mathematica. But you can do that with any other language too, with some work.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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