Permutations of Letters Experiment

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Permutations of Letters Experiment

1. 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.

2. Investigate the number of different permutations of the letters

of the name Lucy.

I am now trying to find the maximum number of possible permutations of

the name LUCY. This name has four letters any four variable letters L,

U, C, and Y.

Permutations:

LUCY ULCY CLYU YLUC

LUYC ULYC CLUY YLCU

LCYU UYCL CULY YCUL

LCUY UYLC CUYL YCLU

LYCU UCLY CYUL YULC

LYUC UCYL CYLU YUCL

This shows us that there are twenty-four possible permutations of the

letters of the name LUCY.

Chose some different combinations of letter.

3. Investigate the number of different permutations of the letters

that you have chosen.

I am now going to try to find a pattern in the permutations of

combinations of different letters.

a) Firstly with one letter. * 1

A

There is one permutation with one letter.

b) With two letters. * 2

AB BA

There are two permutations with two different letters.

c) With three letters. * 3

ABC BAC CBA

ACB BCA CAB

There are six permutations with three different letters.

d) With four letters. * 5

ABCD BACD CABD DABC

ABDC BADC CADB DACB

ACBD BCAD CBAC DBAC

ACDB BCDA CBCA DBCA

ADCB BDAC CDAB DCAB

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