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Investigation To start my investigation I am going to start with something a little easier than Lucy this will help with trying to establish a general pattern and in turn the general formula. I will start with the word IT Name Combinations Number of letters IT IT 2 TI This is very simple the word has 2 letters and 2 possible arrangements for the letters. Now I will try IAN Name Combinations Number of letters IAN IAN 3 INA NIA NAI AIN ANI The number of letters that I have used has now increased to 3 but the number of arrangements has changed it has become 6. I will now try the name LUCY Name Combinations Number of letters LUCY Lucy 4 Luyc Lyuc Lycu Lcyu Lcuy Clyu Cluy Cylu Cyul Cuyl Culy Ucly Ucyl Uycl Uylc Ulcy Ulyc Ycul Yclu Ylcu Yluc Yulc Yucl With Lucy the number of letters has increased to 4 and the number of arrangements has increased to 24. This is a strange result. Ian 3x2x1=6 (number of combinations) Lucy 4x3x2x1= 24 (number of combinations) I can best describe how I came to this theory by using an example involving cards and spaces. If I have 4 cards and four spaces and...

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