Rearranging Letters in a Word
explanatory Essay
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
=======
7) MAME
=======
2)
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The total number of arrangements for the name 'EMMA' is 12.
EMAM
8) MEAM
=======
3) EAMM
=======
9) MAEM
=======
4) MMEA
=======
10) AEMM
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5) MMAE
=======
11) AMEM
========
6) MEMA
=======
12) AMME
========
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
=======
9) NYAD
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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.
3) ADYN
11) NDYA
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19) YADN
========
4) ADNY
=======
12) NDAY
========
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.
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