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**jacks****Member**- Registered: 2012-11-21
- Posts: 80

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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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,576

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

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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