# Emma&#146;s Dilemma

Extracts from this document...

Introduction

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

Middle

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:-

1.aa

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

The 2 different ways are:-

1.jo

2.oj

#letters in name | 0 letters repeating | 1 letter repeating |

2 | 2 | 1 |

3 | 6 | 3 |

4 | 24 | 12 |

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

Conclusion

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 :-

n | shift | x-1 | = |

## 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 1.2.3.4=24

This student written piece of work is one of many that can be found in our GCSE Emma's Dilemma section.

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