# Rearranging Letters in a Word

explanatory Essay
1394 words
1394 words

Rearranging Letters in a Word

For this piece of coursework I am going to investigate the number of

different ways I can write a word, re-arranging the letters without

having any repeats of the sequence.

After I have finished my investigations I will try and use my findings

to draw together a formula which I could then use to find out how many

ways a word can be written for any chosen word.

My initial step is to write the name 'EMMA' with as many different

arrangements I can find.

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Part 1

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1) EMMA

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7) MAME

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2)

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The total number of arrangements for the name 'EMMA' is 12.

EMAM

8) MEAM

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3) EAMM

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9) MAEM

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4) MMEA

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10) AEMM

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5) MMAE

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11) AMEM

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6) MEMA

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12) AMME

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Next I am again going to try a 4 letter word, but this time without

repeats (no 2 letters the same) in it.

I predict that a 4 letter without repeats will have a lot more letter

arrangements than the name EMMA which has 'M' repeated.

Part 2- I have chosen the name ANDY.

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1) ANDY

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17) DYNA

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2) ANYD

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10) NYDA

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18) DYAN

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The total number of arrangements for the name ANDY is 24.

11) NDYA

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12) NDAY

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#### In this essay, the author

• Describes the formulas they could use to find out how many people they had.
• Explains that they are going to try a 4 letter word, but this time without the word.
• Explains that sara would be c/2, where c is repeated in a word.
• Explains that they're going to try a 4 letter word, which has x repeated 3 times.
• Explains that they will try a name with 5 different letters.
• Describes the letters m, a, n, d, and y at the front.
• Explains that they will try a 3 letter word, which has no repeats.
• Opines that there must be a link between how many repeats there are in the summary.
• Explains that they will also record their results so far in the table.
• Explains that a 5 letter word repeated 3 times has 1/3 repeats.
• Describes how they found a topic covering multiplying numbers out i.e.
• Opines that this works but it is not clear what to do with the formula when more information is needed.
• Explains that they could use their formula to work out any word and their last example is summary:
• Describes the factors that determine the size of the sample.
• Explains that their first formula is n! / r! where n is the number of letters in the word and r is a letter repeated.