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Emma’s Dilemma
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| Submitted: Thu Jul 11 2002
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Emma's Dilemma Aim: The aim of this investigation is to study the number of combinations, which can be used for different words. I will examine words where the letters are all different or where there may be more than one repeated letter. I will examine words with different numbers of letters. I will then eventually work out a formula for it. Investigation: In the name LUCY there are four different letters and there are 24 different arrangements: 1. 1. LUCY 2. LUYC 3. LCUY 4. LCYU 5. LYCU 6. LYUC 7. ULYC 8. ULCY 9. UCLY 10. UCYL 11. UYCL 12. UYLC 13. CLUY 14. CLYU 15. CYUL 16. CYLU 17. CUYL 18. CULY 19. YLUC 20. YLCU 21. YCLU 22. YCUL 23. YUCL 24. YULC In the three-letter word SAM, there are 3 different letters and 6 different arrangements: 1. 1. SAM 2. SMA 3. MAS 4. MSA 5. ASM 6. AMS In the two-letter word, MO there are 2 different letters and 2 different arrangements: 1. 1. MO 2. OM Number of all different Letters Number of Different Arrangements 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 If we put all of this...
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