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## #1 2012-12-17 06:15:34

jacks
Member
Registered: 2012-11-21
Posts: 132

### alphebetica order

In how many ways can the letters of the word SPECIAL be permuted if the vowels are to appear in alphabetical order

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## #2 2012-12-17 06:42:41

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: alphebetica order

Aei => 333
Spcl => 24 Ways, So Make It 4444

Start List To Get Idea

posted at 18:43 UTC: (continued)

4444333
4443334
4433344
4333444
3334444

3344443
3344434
3344344
3343444

4334443
4334434
4334344

4433443
4433434

4443343

now do single 3 first then double 3 later...

3444433
3444334
3443344
3433444

4344433
4344334
4343344

4434433
4434334

4443433

now do all 3's apart and separated...

3444343
3443443
3434443

3443434
3434434

3434344

continue with 3 in second place...

4344343
4343443
4343434

now do 3 in third place.

4434343

that's it i think.
hope i didn't miss any.
count them all up and multiply by 24 for the answer to the question because the consonants can be arranged 24 ways = 4 x 3 x 2 x 1.

Last edited by John E. Franklin (2012-12-17 06:51:55)

igloo myrtilles fourmis

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## #3 2012-12-17 07:00:56

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: alphebetica order

I would say there are 4*5*6*7=840 ways...

Last edited by anonimnystefy (2012-12-17 07:03:18)

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