Emmas Dilema
Emma's Dilemma In this investigation, we had to find out the number of different combinations that could be made when different amounts and combinations of letters were formed. This includes repeated patterns of letters. Emma and Lucy wanted to find the amount of different combinations each of their names could make. Emma can be represented by the letters AABC as there is the same amount of letters in both and there is one repeat in both as well. Lucy can be represented by ABCD as it contains 4 different letters with no repeats. I also had to attempt to find a formula to work out the amount of combinations for other amounts of letters. To find out the amount of combinations which can be made by non-repeated or repeated patterns of letters, I started off with a combination which contains the same letters, for example for a repeated pattern of letters AA, and then add letters to that, for example AAB then AABC etc. Combinations with no repeats: A: 1. A AB: 1. AB 2. BA ABC: 1. ABC 2. ACB 3. BAC 4. BCA 5. CAB 6. CBA ABCD: 1. ABCD 2. ABDC 3. ACBD 4. ACDB 5. ADCB 6. ADBC 7. BACD 8. BADC 9. BCAD 10. BCDA 11. BDAC 12. BDCA 13. CABD 14. CADB 15. CBAD 16. CBDA 17. CDAB 18. CDBA 19. DABC 20. DACB 21. DBAC 22. DBCA 23. DCAB 24. DCBA Here is a table of my results: Amount of letters in combination Amount of different combinations made by letters