# Permutations of a Four Letter Word

explanatory Essay
1017 words
1017 words

Permutations of a Four Letter Word

In this piece of coursework my initial aim is to investigate how many

different combinations there are for four letters (e.g. ABCD), I also

intend to develop this to investigate the way in which by altering the

letters to form other kinds of combinations (e.g. ABCC or AAB) the

number is affected. Once I have found the general formulae, I will

apply these to harder situations and this is what I am aiming to do. I

am trying to find the general formulae which can be applied to all

i.e. one letter (e.g.A) moving on to harder problems and by the end I

hope to be able to find the possible arrangements for any given word.

I will do this by using tables and lists of my results to show the

possible combinations and make it easy to compare them and to spot the

pattern and try and turn this into a general formula. Once the initial

formulae have be en discovered I think that it should be much easier

to determine the harder formula, as I will not need to write out as

many tables, to work out these formulae

Results-

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Single different letters-

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1 letter- A

2 letters- AB

BA

3 letters- ABC

ACB

BAC

BCA

CAB

CBA

No. of letters 1 2 3

No. of combinations 1 2 6

This gives the formula =n! - Where n equal the number of letters

Explanation-

============

This is because once you have picked one letter there are then only

two more letters and then one letter. This means that you get 3x2x1

and this gives you 6 which is equal to n!

This formula will allow me to work out the number of combinations of

any word without a repeated letter by using this basic idea I will be

#### In this essay, the author

• Opines that applying these to harder situations is what they are aiming to do.
• Explains that they will use tables and lists of their results to show the results.
• Opines that cab will both be aab and this will be true for all the possible scenarios.
• Explains that if you have a triple letter, then you must divide the n! by 3!
• Explains the fact that you have to divide by 3! instead of 2! and this leads them to summary:
• Explains that we need to use a generalised formula for this.
• Explains that y and z are repeated 4 times and 2 times.
• Opines that in order to do so, we must find out how we arrived at the 3!
• Assumes that ab is the same ba in this process.