Emma’s dilemma

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Emma’s dilemma

    Every name has many ways of arranging the letters e.g. BOB, OBB, BBO. I am trying to find a pattern and formula for finding out how many combinations there for a name. I tried different names with a different number of letters in them, I also tried the names with repeated letters in them. There are several methods of finding out the combinations  of a name, I have used 3 different methods.

Method 1

Listing

Two lettered names

ED

DE

2 ways

Three lettered names

As you can see below a three lettered name with 1 repetion in it has half the number of combinations.

TED

TDE

ETD

EDT

DTE

DET

6 ways

BOB

BBO

OBB

3 ways

Four lettered names

I have noticed that with four lettered names that with 1 letter repeated there are half the number of combinations and halved again if there are two pairs of letters

LUCY              EMMA
LCUY              EAMM

LYCU              EMAM

LCYU              AEMM

LYUC              AMEM

LUYC              AMME

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ULCY              MMAE

ULYC              MMEA

ULYC              MEMA

UYLC              MAME

UCLY              MEAM

UCYL              MAEM

CLUY              12 ways

CLYU

CYUL              LULU

CYLU              LUUL

CUYL              UULL

CULY              ULUL

YLUC              ULLU

YLCU   ...

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