GCSE Mathematics Coursework - Emma's Dilemma

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 GCSE Mathematics Coursework - Emma's Dilemma

Method:

First, I tested different arrangements of the name 'EMMA', by systematically rearranging the letters in the name such as:

1-EMMA        4-AEMM        7-MMEA        10-MEAM

2-EAMM        5-AMME        8-MEMA        11-MAEM

3-EMAM        6-AMEM        9-MMAE        12-MAME

        I found that there were twelve arrangements for the name 'EMMA'. I then investigated different arrangements of letters in the name 'LUCY', using the same method:

        1-LUCY        7-UCYL        13-CYLU        19-YCLU

        2-LUYC        8-UCLY        14-CYUL        20-YCUL

3-LCUY        9-UYLC        15-CUYL        21-YUCL

4-LCYU        10-UYCL        16-CULY        22-YULC

5-LYCU        11-ULCY        17-CLYU        23-YLCU

        6-LYUC        12-ULYC        18-CLUY        24-YLUC

        

        I found that there were many more arrangements in the name 'LUCY' than in the name 'EMMA'. This is because the name 'EMMA' contains repeated letters and the name 'LUCY' does not. I then investigated how many different arrangements of letters there were in other names of different lengths. The lengths of names that I used were 2, 3, and 4 letter names. I recorded my results in a table.

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Table showing the number of different arrangements of letters possible in words of different lengths with no repeated letters

        After recording the results in a table, I found that there was a pattern in my results. The number of arrangements of letters in a 3-letter name without repeated letters is 6, and the number of arrangements in a 2-letter name without repeated letters is 2. There is only one possible arrangement of letters in a 1-letter word.

The number of arrangements of letters in each name increases like this:

1x1=1

1x2=2

1x2x3=6

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