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# In this project I had to find out the number of different ways you could arrange any letter words with no repeats, then with one repeat and then find a formula for any number of repeats.

Extracts from this document...

Introduction

Kate Parkin 10HB

GCSE Coursework

Mathematics

Emma's Dilemma

Introduction

In this project I had to find out the number of different ways you could arrange any letter words with no repeats, then with one repeat and then find a formula for any number of repeats.

All Different Letters

First I decided to do a one letter word:

I

There of course was only one way of arranging it!

Then I did a two-letter word:

Me                Em

There were two ways of arranging that. Next I did a three letter word

You                You

Uoy                Uyo

Oyu                Ouy

After that I decided to do the name Lucy.

Middle

I thought this answer was 24 because there were 4 different letters and 6 different ways to arrange it with the same first letter and so 6x4 is 24

The next name I did was Chloe. I came up with 120 ways of arranging it. For each different first letter there were 24 different ways of arranging the other letters, as ;

Chloe        Chleo        Choel        Cheol        Cheol        Chelo        Cloeh        Clohe        Cleho        Cleoh        Clhoe        Clheo

Coehl        Coelh        Colhe        Coleh        Cohel        Cohle        Ceolh        Ceohl        Cehlo        Cehol        Celho        Celoh

So there would be a total of 24 x 5 = 120 ways of arranging the letters.

The Formula

Next I wrote out a table with my results in it:

All Different

Letters                        Ways

1. 1
2. 2
3. 6
4. 24
5. 120

Then with this table I worked out a  formula for words with no repeats.

Conclusion

Formula For All Different Number Of Repeats

I then decided that as for one repeat it was the first answer divided by two for two repeats it must be divided by 6 (divided by two and then that answer divided by three). Then for three repeats it would be divided 24 (divided by two then that answer by three and then that answer by four). And so on.

Conclusion

As this was my first piece of Maths coursework I found it quite tricky, but after I got over that I managed to do quite well at it. I however, did find this piece of coursework interesting and challenging and I'm looking forward to my next piece.

This student written piece of work is one of many that can be found in our GCSE Emma's Dilemma section.

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