Arranging Letters
Firstly we arrange EMMA's Name.
1)EAMM 7)MAEM
2)EMAM 8)MAME
3)MEMA 9)AMME
4)MEAM 10)AEMM
5)MMEA 11)AMEM
6)MMAE 12)EMMA
.
.
Secondly we arrange Lucy's name.
1)Lucy 12)Cyul 22)Yulc
2)Luyc 13)Culy 23)Ycul
4)Lycu 14)Culy 24)Yluc
5)Lcuy 15)Cylu 25)Ucyl
6)Lcyu 16)Clyu
7)Ulcy 17)Cuyl
8)Ucly 18)Yluc
9)Uycl 19)Yucl
10)Ulyc 20)Yclu
11)Uylc 21)Ylcu
From these 2 investigation I worked out a method, To Use My Method I
Preferred To Convert Letters into Numbers, It Makes No Difference:
Step1: 1234---Do the last two number first then you get 1243.
1243---Do the last three numbers and try the possibility. 1423. 1432.
1342.1324, because the number 2 has been the first number of last
three numbers, so we don't do it again.
Step2: we have list all arrangements of 1 go front, so we do 2 go
front. 2134 and we do same thing to it, it will look like this:
2134---2143, 2143---2431,2413,2314,2341
Step3: We have finished 2 go first, then let's do 3 go ahead.
3124---3142, 3142---3241,3214,3412,3421
Step4: We have finished 3 go ahead, then try 4
4123---4132, 4132---4231,4213,4312,4321
We have list all arrangement of 1234, use this method we can arrange
the number which has 5 figures or more.
We are trying to work out a formula which can calculate the number of
arrangement when we look at a number.
Let's list all the arrangement for 1234:
1234 4123
1243 4132
1324 --- 6 arrangement 4231 ---- 6 arrangement
1342 4213
1432 4321
1423 4312
2134 3124
2143 3143
2341 ---- 6 arrangements 3241 --- 6 arrangements
2314 3214
2413 3412
2431 3421
So if we multiply 6 by 4, we would get 24, and we can get the total
arrangements of 24.
Let's try 5 figures:
12345 13245
12354 13254
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Once we squared both sides the square root will cancel each other out, and the 6^2 will then become 36.
letters in it. I will also try and find a formula to find the total
E.g. 5! = 5 x 4 x 3 x 2 x 1 5! = 120.
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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.
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