# Emma's Dilemma

Extracts from this document...

Introduction

Richard Hanton Mathematics – Coursework Page of

08/05/07

Emma’s Dilemma

- Investigate the number of different permutations of the letters of the name Emma.

I am trying to find the maximum number of possible permutations of the name EMMA. This name has four letters but only three variable letters E, M and A.

Permutations:

EMMA MMAE AEMM

EMAM MMEA AMEM

EAMM MAME AMME

MAEM

MEMA

MEAM

This shows us that there are twelve possible permutations of the letters of the name EMMA.

Emma has a friend called Lucy.

- Investigate the number of different permutations of the letters of the name Lucy.

Middle

ABDCE BADCE CADBE DACBE EACBD

ABDEC BADEC CADEB DACEB EACDB

ABECD BAECD CAEBD DAEBC EADBC

ABEDC BAEDC CAEDB DAECB EADCB

ACBDE BCADE CBADE DBACE EBACD

ACBED BCAED CBAED DBAEC EBADC

ACDBE BCDAE CBDAE DBCAE EBCAD

ACDEB BCDEA CBDEA DBCEA EBCDA

ACEBD BCEAD CBEAD DBEAC EBDAC

ACEDB BCEDA CBEDA DBECA EBDCA

ADBCE BDACE CDABE DCABE ECABD

ADBEC BDAEC CDAEB DCAEB ECADB

ADCBE BDCAE CDBAE DCBAE ECBAD

ADCEB BDCEA CDBEA DCBEA ECBDA

ADEBC BDEAC CDEAB DCEAB ECDAB

ADECB BDECA CDEBA DCEBA ECDBA

AEBCD BEACD CEABD DEABC EDABC

AEBDC BEADC CEADB DEACB EDACB

AECBD BECAD CEBAD DEBAC EDBAC

AECDB BECDA CEBDA DEBCA EDBCA

AEDBC BEDAC CEDAB DECAB EDCAB

AEDCB BEDCA CEDBA DECBA EDCBA

There are 120 permutations with five different letters

My prediction was correct.

Conclusion

Therefore I predict that the number of permutations for AABBC will be:

P = _ 5! _ = 120 = 30

2! x 2! x 1! 4

Where T = 5

L1 = 2

L2 = 2

Ln = 1

With two pairs of repeating letters and one different letter.

AABBC BBAAC CAABB

AABCB BBACA CABAB

AACBB BBCAA CABBA

ABABC BAABC CBAAB

ABACB BAACB CBABA

ABBAC BABAC CBBAA

ABBCA BABCA

ABCAB BACAB

ABCBA BACBA

ACABB BCAAB

ACBAB BCABA

ACBBA BCBAA

There are thirty permutations with two pairs of repeating letters and one different letter.

My prediction was correct.

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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