Name: Jo
Total number of letters: 2
jo
oj
Jo has 2 different combinations.
Name: Ian
Total number of letters: 3
ian
ina
ani
ain
nai
ain
Ian has 6 different combinations. I have realised that the total number of combinations is the number of letters multiplied by the previous number of combinations.
Name: Lucy
Total number of letters: 4
Previous number of combinations: 6
Prediction: 4 x 6 = 24
lucy
luyc
lcyu
lcuy
lycu
lyuc
ulcy
ulyc
uylc
uycl
ucly
ucyl
cluy
clyu
culy
cuyl
cyul
cylu
yluc
ylcu
yclu
ycul
yucl
yulc
As i predicted 24 combinations. Therefore I can predict the name Rosie will have 120 combinations.
Name: Rosie
Total number of letters: 5
Previous number of combinations: 24
Prediction: 5 X 24 = 120
rosie
rosei
roise
roies
roesi
roeis
rsioe
rsieo
rsoie
rsoei
rseoi
rseio
risoe
riseo
riose
rioes
rieso
rieos
resio
resoi
reiso
reios
reois
reosi
This means that I can work out the total number of combination by factorial notation.
I realised this because if I could find the total number of combinations by multiplying the total number of letters by the previous number of combinations it was the same as multiplying the total number of letters by its previous consecutive numbers Factorial Notation.
This means when a name has all letters different with any amount of total letters, I can work out the total number of combinations by using this formula.
Number of combinations = Total number of letters Factorial
C = t !
Ian
Total number of letters = 3
C = 3 !
3 ! = 3 x 2 x 1
3 ! = 6
C = 6
The formula to find out the total number of combinations for any name when all the letters are the same is: Number of combinations = Total number of letters Factorial
C = t !
Having found a formula for Lucy when all the letters are different, I am now going to try to develop the formula for Emma, when 2 of the letters are the same.
I looked at other names with different total numbers and put the results in the table below.
I am now going to look at finding a formula for 2 letters the same in a name because the formula must be based on the same principle as the one for all letters different, I am going to start by working out the number of letters factorial, and look for a relationship between this number and the total number of combinations.
The difference between the total number of combinations and the total number of letters factorial is always total number of letters factorial divided by 2.
Therefore the formulae for the total number of combinations when 2 letters are the same is:
Combinations = total number of letters factorial / 2
C = t ! / 2
For Emma
C = 4 ! / 2
C = 12
This means I can predict the total amount of combinations for the name Jenny.
Combinations = total number of letters factorial / 2
Combinations = 5 ! / 2
Combinations = 60