Combination Determination

Question

I have a booth that sells 3 items - Item A, B, and C.

 

I have 50 of each item. 

 

A) How would I determine every possible combination of A, B, and C, including multiples (i.e. AAA, ABB, etc.)?

B) How do I determine possible combinations for larger groups, up to 10 items? (AAAAAAAAAB, ABBBBCCCCC, etc)

 

C) If A is $50, B is $20, and C is $10, how do I find all combinations with a price range (such as 3 items from price range $80-$150) 

 

Answer 1

1)  Three choices for 1st item, three choices for 2nd item, 3 choices for 3rd item.

      3 x 3 x 3 = 27

 

     AAA    BAA    CAA

     AAB    BAB    CAB

     AAC    BAC    CAC

     ABA    BBA    CBA

     ABB    BBB    CBB

     ABC    BBC    CBC

     ACA    BCA    CCA

     ACB    BCB    CCB

     ACC    BCC    CCC

 

B) 3 choices for 1st item, 3 choices for 2nd item, 3 choices for 3rd item, etc etc etc, 3 choices for 10th item

       3^10 = 59049

 

  In general, for N items, it shall be 3^N

 

C) 80 <= 50A + 20B + 10C <= 150 must hold for some ordered triplet (A,B,C)