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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"Learning Why 6x9=54." Opposing Viewpoints in Context. N.p., 31 Dec. 2011. Web. 1 Dec. 2013.
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By using combinations from the above – But this approach has to be made with caution, because confusion can appear in the message.