Different Arrangements for the Letters in the Name Lucy

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Different Arrangements for the Letters in the Name Lucy

I am going to investigate the number of different arrangements for the

letters in the name LUCY

1 arrangement

LUCY

A different arrangement is:

LUYC

Another arrangement is:

LCUY

This combination consists of all the letters being different. I will

also try and find a formula for this arrangement, and number of

letters. Once I have discovered these formulae I am going to

investigate, other combinations of letters and different amounts of

letters. I will then try to discover a link between the formulae to

enable me to find a formula for the general case.

ARRANGEMENTS IN THE NAME LUCY

LUCY UCYL CYUL YCUL

LUYC UCYL CYUL YCUL

LCUY ULCY CULY YUCL

LCYU ULYC CUYL YUCL

LYUC UYCL CLYU YLCU

LYCU UYLC CLUY YLUC

There are 24 different possibilities in this arrangement of 4 letters

all different. I have noticed that with Lucy beginning each different

letter. For example there are 6 arrangements with LUCY beginning with

L, and 6 beginning with u and so on 6*4(the amount of letters) gives

24. This means that all names with 4 different letters will have a

total of 24 different combinations.

I realised that the total number of combinations is the number of

letters multiplied by the previous number of combinations.

Name: Ian

Total number of letters: 3

Previous number of combinations: 2

3 X 2 = 6

Name: Lucy

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Total number of letters: 4

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Previous number of combinations: 6

4 X 6 = 24

This means that I can work out the total number of combination by

factorial notation. Factorial notation is a number multiplied by the

previous consecutive numbers:

E.g. 5! = 5 x 4 x 3 x 2 x 1 5! = 120.

Factorial notation is symbolised using an exclamation mark!

I realised this is because if I could find the total number of

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