By arranging the letters in this way, I found that the four-lettered word LUCY had a total of 24 arrangements. By showing how many arrangements there were when the single letter L was at the beginning I could calculate the total amount of arrangements for the three remaining letters U, C And Y. If I then multiplied the number six (number of arrangements) by the number four (total amount of letters in the word) I could calculate the amount of arrangements for the whole equation. Then i could get the total amount of arrangements.
4 x 6 = 24
i can use this equation to calculate the area of a rectangle. Height x width. But in this case the height was the number of arrangements with any-one letter at the beginning and the width was the total amount of letters in anyone word.
To prove this I have began testing it on the five-letter name JAMIE.
Five-Lettered Word
JAMIE - JAMIE, JAMEI, JAEIM, JAEMI, JAIME, JAIEM
JMAIE, JMAEI, JMEIA, JMEAI, JMIEA, JMIAE
JIAME, JIAEM, JIEMA, JIEAM, JIMEA, JIMAE
JEAMI, JEAIM, JEIMA, JEIAM, JEMAI, JEMIA
Using this formula I have explained, I can use this rule to work out the total number of arrangements. There are for the five letters word JAMIE. I know there are twenty- four arrangements when the single letter J is at the beginning, I can now multiply this by five (number of letters in the word) and get the total nunber of ways.
24 x 5 = 120
J A M I E
24 24 24 24 24
1 1
2 2
3 6
4 24
5 120
6 720
The number of different letters multiplied by the previous number of arrangements equals the total amount of arrangements for the next of letters. This can be shown as 720 x 6 .
This is a table to show this:
Four-Lettered Word- Two of any one letter
EMMA MEMA MEAM AMME
EMMA MEMA MEAM AMME
EAMM MMEA MMAE AMEM
EAMM MMEA MMAE AMEM
EMAM MAME MAEM AEMM
EMAM MAME MAEM AEMM
I have found out that from any four-lettered word i will get 24 different arrangements.
I will check doubled words.
For a 4 Lettered word there are 24 arrangements in total, as my results show, next i will investigate is the results of having two of the same letters in any-one word and its effects on the outcome of the number of arrangements. I will firstly look at the four-lettered name Emma. As you can see two of its letters are the same therefore we have to treat them as one. If we treat this letter S as individuals we see there are 24 arrangements as none of them are the same. But if we treat it as a double we notice each arrangement has been quoted twice. This is why, in order to receive the correct amount arrangements we need to divide it by the number in which the identical letters occur. Its the number two.
Formula
This formula can be used to work out as many letter repeats, as you like.EXAMPLE
Banana
In the word banana there are 6 letters altogether making it 6x5x4x3x2x1, which is equal to the formula of 6! There are 3 A’s repeated and also 2 N’s. Also there is one b.! In the formula.
This is 6! ÷ 3! ÷ 2!
Conclusion/evaluation
It is possible to see from my research that overall as the number of letters in a word increases, the number of combinations increases. If a letter is repeated in a word, that word has less combinations than another word of equal length with no repeated letters. If i did the experiment again i would spend more time with more variety of names. i would use more double letters and look for anu other formulaes.This would mean that into more detail and check the formula for the larger words.
