Emma's Dilemma

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Emma’s Dilemma – Mathematics Coursework

Scott McMenemy

  • Emma and Lucy are playing with the different arrangements of the letters of their names. There are a number of different arrangements in the letters of Lucy’s name:

LUCY   ULCY   CYUL   YLUC

LUYC   ULYC   CYLU   YLCU

LYUC   UYLC   CLUY   YCLU

LYCU   UYCL   CLYU   YCUL

LCYU   UCLY   CULY   YUCL

LCUY   UCYL   CUYL   YULC

There are an overall 24 different arrangements for the letter in Lucy’s name.

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  • There are a number of different arrangements for the letters od Emma’s name also:

EMMA   MEMA   AMME

EMAM   MEAM   AMEM

EAMM   MMEA   AEMM

               MAME

               MAEM

               MMAE

There are an overall 12 different arrangements for the letters in Emma’s name.

  • I have discovered that there are 24 arrangements for any 4 letter word as long as all letters are different – e.g. Lucy, Fred, John.

Taking n as the ...

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