Investigating Different Arrangements of Letters of Words
I will be investigating the different arrangements of letters of
words, which don't have any identical letters in them and those that
do. Then I will try and find a formula that can calculate the total
arrangements of letters of any word, which does not have any identical
letters in it. I will also try and find a formula to find the total
arrangements of words, which have some identical letters in them.
Firstly I will look at those words, which have no identical letters in
them and then work out a formula that can find the total arrangements
of letters in them. So I will begin by finding the total arrangements
of a one-lettered word to finding the total arrangements of a
four-lettered word. Thereafter I will try and predict the total
arrangements of a five-lettered word and then I will check if I was
correct by finding the total arrangements of it's letters
Part 1
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One-lettered word
A =1
There is only one arrangement for a one-lettered word.
Two-lettered word
WE
EW =2
There are two different arrangements for a two-lettered word whose
letters are all different.
Three-lettered word
CAR CRA
ACR ARC =6
RCA RAC
There are six different arrangement for a three-lettered word whose
letters are all different.
Four-lettered word
LUCY LUYC LYUC LYCU LCYU LCUY
ULCY ULYC UCLY UCYL UYCL UYLC
CLUY CLYU CULY CUYL CYUL CYLU
YUCL YULC YCUL YCLU YLCU YLUC =24
There are 24 different arrangement for a four-lettered word whose
letters are all different.
In a four-lettered word the total arrangements is 24 because in the
word LUCY there are 4 letters and you can only get 6 different
arrangements with each letter at the beginning. So the calculations
for this would be 4 x 6 = 24.
For a five-lettered word there are 24 different arrangements with each
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