You are not logged in.
Pages: 1
Find all possible arrangements of the word PIGEON so that the vowels are in alphabetical order.
Offline
EIOPGN PEIOGN PGEION PGNEIO EPIOGN EIPOGN
EIOPNG PEIONG PNEIOG PNGEIO EPIONG EIPONG
EIOGPN GEIOPN GPEION GPNEIO EGIOPN EIGOPN
EIOGNP GEIONP GNEIOP GNPEIO EGIONP EIGONP
EIONPG NEIOPG NPEIOG NPGEIO ENIOPG EINOPG
EIONGP NEIOGP NGEIOP NGPEIO ENIOGP EINOGP
EPGION EPGNIO EIPGON EIPGNO PEIGNO PGEINO
EPNIOG EPNGIO EIPNOG EIPNGO PEINGO PNEIGO
EGPION EGPNIO EIGPON EIGPNO GEIPNO GPEINO
EGNIOP EGNPIO EIGNOP EIGNPO GEINPO GNEIPO
ENPIOG ENPGIO EINPOG EINPGO NEIPGO NPEIGO
ENGIOP ENGPIO EINGOP EINGPO NEIGPO NGEPIO
Thats all I can be bothered to do. There is more....
Edit: Assuming Mathsyperson is right, then there is another 48
Ok I might as well add the rest (thaks mathsy):
EPIGON EPIGNO EPGINO PEIGNO PEGION PEGINO
EPINOG EPINGO EPNIGO PEINGO PENIOG PENIGO
EGIPON EGIPNO EGPINO GEIPNO GEPION GEPINO
EGINOP EGINPO EGNIPO GEINPO GENIOP GENIPO
ENIPOG ENIPGO ENPIGO NEIPGO NEPIOG NEPIGO
ENIGOP ENIGPO ENGIPO NEIGPO NEGIOP NEGIPO
PEGNIO PGENIO
PENGIO PNEGIO
GEPNIO GPENIO
GENPIO GNEPIO
NEPGIO NPEGIO
NEGPIO NGEPIO
That's all 120.
Last edited by Daniel123 (2007-06-01 04:31:34)
Offline
...Except that there's an I in there as well, that also needs to be ordered correctly.
So the actual answer is 6!/6 = 120.
Edit: Daniel's well on the way to showing the list exhaustively. By the way he's grouped them, it's obvious that there are 6 combinations for every way that you can specifically place the E, I and O.
eg. there are 6 of the form EIO###, 6 of the form EI#O##, etc.
In addition to what he's already got, the additional forms are:
E#I#O#
E#I##O
E##I#O
#EI##O
#E#IO#
#E#I#O
#E##IO
##E#IO
Daniel had 12 forms and I've added another 8, so that means that there are (12+8)x6 = 120 combinations again.
Last edited by mathsyperson (2007-06-01 04:16:56)
Why did the vector cross the road?
It wanted to be normal.
Offline
Right, thanks everyone
Offline
Here is the general case. Suppose you have n letters (all distinct) and you want to find the number of permutations in which r of them are ordered in a specific way.
Well, you first choose r spots from the n places in which to put your r letters in their specific order. This can obviously be done in [sup]n[/sup]C[sub]r[/sub] ways. For each of these [sup]n[/sup]C[sub]r[/sub] placements, the other n−r letters can be placed in the other spots in (n−r)! ways. Hence the total number of ways of arranging n letters with r of them in a specific order is
Last edited by JaneFairfax (2007-06-02 07:10:48)
Offline
Pages: 1