What is the max number of combinations using A, B, C, D, E, and F.?

I will give you an example using A, B, and C:


A B C can make A, B, C, AB, AC, BC, and ABC.


AB = BA.


I would like to know the max number of combinations, and if possible(if you have time), all of the combinations. This is not for a homework assignment, I just want to know.

What is the max number of combinations using A, B, C, D, E, and F.?
2^6 - 1 = 63 ways.





Basically, you can either have the letter in the combination or not. So there are two possibilities for each letter. Using the General Counting Principle, you would multiply each of these possibilities, so 2*2*2*2*2*2 = 2^6. However, there is one combination where none of the letters are selected, so that's why you subtract 1.





edit: The above answerer has it now, only in a different way. Rodent, the order doesn't matter, and he wants to know how many ways you select a different number of letters.





Here's the list:





1. A


2. B


3. C


4. D


5. E


6. F


7. AB


8. AC


9. AD


10. AE


11. AF


12. BC


13. BD


14. BE


15. BF


16. CD


17. CE


18. CF


19. DE


20. DF


21. EF


22. ABC


23. ABD


24. ABE


25. ABF


26. ACD


27. ACE


28. ACF


29. ADE


30. ADF


31. AEF


32. BCD


33. BCE


34. BCF


35. BDE


36. BDF


37. BEF


38. CDE


39. CDF


40. CEF


41. DEF


42. ABCD


43. ABCE


44. ABCF


45. ABDE


46. ABDF


47. ABEF


48. ACDE


49. ACDF


50. ACEF


51. ADEF


52. BCDE


53. BCDF


54. BCEF


55. BDEF


56. CDEF


57. ABCDE


58. ABCDF


59. ABCEF


60. ABDEF


61. ACDEF


62. BCDEF


63. ABCDEF
Reply:I know this is a 10 month old "Answer", but how exactly did you look at this, I get 3600 combinations from A,B to F,E,D,C,B,A Report It

Reply:6+5+4+3+2+1= 21





no, no. how 'bout:





6 +6*5/(1*2) + 6*5*4/(1*2*3) +6*5*4*3/(1*2*3*4) +6*5*4*3*2(1*2*3*4*5) +1





6+15+20+15+6+1 = 63
Reply:6! which would be 6*5*4*3*2*1





which is 30*4*3*2


120*3*2


360*2


720?
Reply:AB


AC


AD


AE


AF


BC


BD


BE


BF


CD


CE


CF


DE


DF


A


B


C


D


E


F


ABCDEF


ABC


ABD


ABE


ABF


ACE


ACE


ACF


CDE


CDF


DEF

marguerite