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 LLUU
YCLU 6 ways
YCUL
YUCL
YULC
24 WAYS
Since five lettered names have a far greater number of combinations, I will use another way of listing them, I have noticed that CLARK has a four lettered word after the C with no letters repeated, so CLARK beginning with a C must have 24 combinations, therefore must be the same with the word beginning with L, A, R AND K.
CLARK PETER BOBBY
C 24 P 12 B 12
L 24 E24 O 4
A 24 T12 Y 4
R 24 R12 20 WAYS
K 24 60 WAYS
120 WAYS
6 lettered names
ROBERT WILLIE THOMAS
R120 W30 T120
O60 I 60 H120
B60 L60 O120
E60 E30 M120
T60 180 WAYS A120
360 WAYS S120
720 WAYS
7 LETTERED NAMES
WILLIAM PHILLIP
W180 P 180
I 360 H 90
L 360 I 180
A 180 L 180
M 180 630 WAYS
1260 WAYS
Method 2
Probability
If there was a bag with 3 pieces of paper in it 1 with t, 1 with e and 1 with d the chances of getting the letters in order is 1/6 because the chances of getting t the first time is 1/3, if you do get the t then there is only 2 pieces left in the bag so getting e the first time after removing the t from the bag is ½ then after that chances of getting the d is 1/1.
2 LETTERED NAMES
ED
½ x 1/1 = ½ =2 WAYS
3 LETTERED NAMES
TED
1/3 x ½ X 1/1 = 1/6 = 6 WAYS
BOB
2/3 X 1/2 X 1/1 = 2/6 = 1/3= 3 WAYS
4 LETTERED NAMES
LUCY
¼ x 1/3 x ½ x 1/1=1/24 =24 ways
EMMA
¼ x 2/3 x ½ x 1/1 =1/12 =12 ways
LULU
2/4 x 2/3 x ½ x 1/1 =1/6 =6 ways
5 LETTERED NAMES
CLARK
1/5 x 1/4 x 1/3 x 1/5 x 1/2 x 1/1 =1/120 =120 ways
PETER
1/5 x 2/4 x 1/3 x 1/2 x 1/1 = 2/120 = 60 ways
BOBBY
3/5 x 1/4 x 2/3 x 1/2 x 1/1 =6/120 =120 ways
6 LETTERED NAMES
ROBERT
2/6 x 1/5 x ¼ x 1/3 x 1/2 x 1/1 =2/720 =360 ways
WILLIE
1/6 x 2/5 x 2/4 x 1/3 x 1/2 x 1/1 = 2/720 = 180
THOMAS
1/6 x 1/5 x 1/4 x 1/3 x 1/2 x 1/1= 1/720 =720 ways
7 LETTERED NAMES
WILLIAM
1/7 x 2/6 x 2/5 x 1/4 x 1/3 x 1/2 x 1/1
PHILLIP
2/7 x 1/6 x 2/5 x 2/4 x 1/3 x 1/2 x 1/1
Method 3
Factorial
! is the symbol in maths for factorial, this means the number multiplied by all the numbers before it up to 0 e.g. 5! Would be 5x4x3x2x1.
2 LETTERED NAMES
ED
½! = 2 WAYS
3 LETTERED NAMES
TED
1/3! =3 WAYS
BOB
2!/3!= 2/6 =1/3 = 3 WAYS
4 LETTERED NAMES
LUCY
¼!= 24 WAYS
EMMA
2!/4!= 2/24 = 12 WAYS
LULU
2!x2!/4!= 4/24 =6 ways
5 LETTERED NAMES
CLARK
1/5!=120 WAYS
PETER
2!/5!=60 WAYS
BOBBY
3!x2!/5!= 20 WAYS
6 LETTERED NAMES
ROBERT
2!/6!=360 WAYS
WILLIE
2!x2!/6!=180WAYS
THOMAS
1/6!= 720 WAYS
7 LETTERED NAMES
WILLIAM
2!x2!/7!=1260 WAYS
PHILLIP
2!x2!x2!/7!= 630 ways
From all the lists I have made I was able to find the formula
E.g. 5 3
xxxxx yyy the equation for this would be (5+3)!/5!x 3!
So if there are x amount of Xs and y amount of Ys e.g.
X y
(xxxx…..x)(yyyy….y) the formula would be (x+y)!/X! x Y!
The final formula to work out how many combinations there are in a name is
(X+Y)!
~~~~~~
X! x Y!