# Emma's Dilemma

Satisfactory Essays
Emma's Dilemma

I am investigating the number of different arrangements there will be

in different types of names. Some names I will investigate on will

have no identical letters such as LUCY. Some will have a pair of

identical letters such as EMMA. Some names will have different

quantities of letters such as AMMIE, JOE and ANNE.

Firstly, I’ll produce a method which will help me figure out the

different arrangements in the name EMMA and LUCY without using any

formulas. Using this method I’ll test all my predictions.

I’ll create formulas for different types of names. Examples are names

with no identical letters, a pair or more identical letters and names

that have 2 different groups of identical letters

Throughout the investigation I will devise different formulas for

working out different types of names. By using one of these formulas

I’ll figure out the total number of arrangements of the letters

XX……XXYY…….Y.

To start of the investigation I have to find the different

arrangements of letters in the name EMMA and LUCY without the use of

any types of formulas. Therefore, I have developed my own method.

Method

1. Write the name in its original format. In this case it will be EMMA

or LUCY.

2. Start with the first letter in the original format (E in EMMA and L

in LUCY) and rearrange the remaining letters in a random order in

front of the first letter.

3. Starting with the first letter, rearrange the last 2 letters of the

name. If the last two letters are identical rearrange the letter

before it (do not rearrange identical letters). Once you have

rearranged the name starting with first letter “E” to the fullest,

write down the total arrangements at the bottom of the work. Then

start of the process again with the second letter in the name acting