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Lucy's Dilemma  

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Lucy was playing with her name. She sees the there are a number of different combinations. These are: 1. LUCY 2. LUYC 3. LCUY 4. LCYU 5. LYUC 6. LYCU 7. ULCY 8. ULYC 9. UCLY 10. UCYL 11. UYLC 12. UYCL 13. CLUY 14. CLYU 15. CULY 16. CUYL 17. CYLU 18. CYUL 19. YLUC 20. YLCU 21. YULC 22. YUCL 23. YCLU 24. YCUL I noticed that the amount of combinations was 4 factorial (i.e. 4x3x2x1), written 4!. I tried with other names and found there to be a pattern. I used Ben, Henry, and Thomas. The numbers were: For Ben, 6 or 3!; For Henry, 120 or 5!; and for Thomas, 720 or 6!. I realised the formula for this was: n! This is because, e.g. for 5, there are 5 possibilities for the first column, 4 for the second, 3 for the third, 2 for the forth, and 1 for the fifth. Then Lucy played around with her friend, Emma's, name. She writes down the different combinations: 1. EMMA 2. EMAM 3. EAMM 4. MEMA 5. MEAM 6. MMEA 7. MMAE 8. MAEM 9. MAME 10....

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