Permutation of Letters

803 Words2 Pages

Permutation of Letters

EMMA is investigating the amount of different arrangements of letters

in her name; she does the same with her friend LUCY. LUCY has twice as

many arrangements as EMMA, they are curious as to why this is and

decide to investigate other names and find reasons for their answers.

EMMA -

emma,

eamm,

emam,

aemm,

amme,

amem,

meam,

maem,

mame,

mema,

mmea,

mmea,

LUCY -

lucy,

luyc,

lycu,

lyuc,

lcyu,

lcuy,

ulcy,

ulyc,

uylc,

uycl,

ucly,

ucyl,

cluy,

clyu,

culy,

cuyl,

cyul,

cylu,

yluc,

ylcu,

yulc,

yucl,

yclu,

ycul,

[IMAGE]

24

[IMAGE]12

Emma has 12 combinations and Lucy has 24. ½ of 24 = 12 so Emma has

half the amount that Lucy has; this may be because Emma has 2 letters

the same. I will be investigating whther this happens to other names

as well.

I will Investigate -

· The amount of combinations for names with 2-10 letters

· What happens when those names have 2 letters the same

· What happens when they have 2,3,4,5 etc. letters the same

· Whether 3 letters the same means 1/3 of the combinations it would

have if no letters were the same

· Whether 4 letters the same means 1/4 of the combinations it would

have if no letters were the same (and 5, 6 ,7 etc.)

· Whether there are any patterns or rules to follow when estimating

amounts of combinations

· What happens when words have more than 1 letter twice (e.g. LIANNA)

2 letter - 0 same = 2

JO,

OJ

2 letters - 2 same = 1

DD

3 letters - 0 same = 6

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