Emma's Dilemma.

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Emma's Dilemma

Emma's Dilemma

In my investigation I am going to investigate the number of different arrangements of letters in a word.

e.g.

Tim

Is one arrangement

Mit

Is another

First I am going to investigate how many different arrangements in the name LUCY, which has no letters the same.


LUCY

LUYC

LYCU

LYUC

LCYU

LCUY

ULCY

UCLY

UYLC

ULYC

UCYL

There are 4 different letters and there are 24different arrangements.

SAM

SMA

MSA

MAS

ASM

AMS

There are 3 different letters in this name and 6 different arrangements.

JO

OJ

There are 2 different letters in this name and there are 2 different arrangements.


UYCL

YCUL

YUCL

YULC

YLCU

YLUC

CYLU

CYUL

CUYL

CULY

CLUY



Table of Results

From the table of results I have found out that a 2 letter word has 2 arrangements, and a 3 letter word has 6.

Taking for example a 3 letter word, I have worked out that if we do 3 (the length of the word) x 2 = 6, the number of different arrangements.

In a 4 letter word, to work out the amount of different arrangements you can do 4 x 3 x 2 = 24, or you can do 4!, which is called 4 factorial which is the same as 4 x 3 x 2.

So, by using factorial (!) I can predict that there will be 40320 different arrangements for an 8 letter word.

The formula for this is: n! = a

Where n = the number of letters in the word and

a = the number of different arrangements.

Now I am going to investigate the number of different arrangements in a word with 2 letters repeated, 3 letters repeated and 4 letters repeated.

EMMA

AMME

AMEM

EMAM

AEMM

EAMM

MMEA

MMAE

MEMA

MAME

MEAM

MAEM

4 letter word, 2 letters repeated, 12 different arrangements.

MUM

MMU

UMM

3 letter word, 2 letters repeated, 3 different arrangements.

Join now!


PQMMM

PMQMM

PMMQM

PMMMQ

QPMMM

QMPMM

QMMPM

QMMMP

MPQMM

MPMQM


MPMMQ

MQPMM

MQMPM

MQMMP

MMPQM

MMQMP

MMMPQ

MMMQP

MMPQM

MMMQP


5 letter word, 3 letters repeated, 20 different arrangements.

SMMM

MSMM

MMSM

MMMS

4 letter word, 3 letters repeated, 4 different arrangements.

RRRRK

RRRKR

RRKRR

RKRRR

KRRRR

5 letter word, 4 letters repeated, 5 different arrangements.

Table of Results

I have worked out that if you do say 5! = 120, to find out how many different arrangement in a 3 letter word it would be 5! Divided by 6 = 20, so, a 6 letter word ...

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