- There are a number of different arrangements for the letters od Emma’s name also:
EMMA MEMA AMME
EMAM MEAM AMEM
EAMM MMEA AEMM
MAME
MAEM
MMAE
There are an overall 12 different arrangements for the letters in Emma’s name.
- I have discovered that there are 24 arrangements for any 4 letter word as long as all letters are different – e.g. Lucy, Fred, John.
Taking n as the number of letters in the word, we can say that the number of arrangements for a word which has all different letters in n factorial, or n! We can use the name FRED as an example. The numbers of arrangements are shown below:
FRED RFED EFRD DFRE
FRDE RFDE EFDR DFER
FDRE RDFE EDFR DRFE
FDER RDEF EDRF DREF
FEDR REDF ERDF DEFR
FERD REFD ERFD DERF
Factorial is used because for the first choice letter of the word, there are ‘n’ choices, and for the second letter there are ‘n-1’ choice, and for the third letter there are ‘n-2’ choices, taking n as the number of letters in the word. This process will continue until the last letter of the word is dealt with. A table, using the 4-letter word of LUCY as an example, is shown below.
……………………………………………………………………………...
- I discovered that there are 12 arrangements for any word which has 4 letters in which 2 of the 4 are the same. E.g. Lucy, Anne.
The example of ‘Anne’ is shown below:
ANNE NANE ENNA
ANEN NENA ENAN
AENN NNEA EANN
NNAE
NEAN
NAEN
As you can see, there are 12 different arrangements for the letters in the name Anne. To show how many arrangements there are for a word with any number of letters where 2 of them are the same, we can use the formula n!/2.
