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Emma’s Dilemma

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Denise Shaw

Maths Coursework

Emma’s Dilemma

I am using the name Emma playing with the letters in the name to make different arrangements. Emma is a 4 letter word I should get 24 different ways of writing it but because it has 2 letters the same I will only get 12 different ways of writing it.

The ways are:-

1.emma     7.mmae

2.eamm     8.mema

3.emam     9.mame

4.meam    10.aemm

5.maem    11.amme

6.mmea    12.amem

I am now going to use the word Lucy, Lucy also has 4 letters in it but because

...read more.


3.mto   6.omt

Now I am going to use AA a 2 letter word with 2 letters the same, I will get 1 arrangement.

The 1 arrangement is:-


And Jo a 2 letter word with no letters the same gives 2 different ways.

The 2 different ways are:-



#letters in name

0 letters repeating

1 letter repeating










I predict that if I do a 5 letter word with 2 letters the

...read more.


9.dnyna     19.anydn    29.naynd    39.nnady    49.yannd    59.ynadn

10.dnnya   20.anynd   30.nadny     40.nnday    50.yandn    60.ynnda

I predict for a 6 letter word with no letters the same I would get 720 different arrangements. The way to do this is start from 1 and go all the way up to 6 and times them all together and you get the answer for example 1X2X3X4X5X6 =720 arrangements.

To find out the answer on a calculator the formula is :-





This is called factorial

Factorial is the product of all the positive ategers from 1 to a given number for example 4 factorial, usually written 4! Is product

...read more.

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