Help with countinig principle
 

Hi I was wondering if someone could take a look at this. I am currently doing a project on horse racing and I am
stuck on a piece of programming logic. The piece I am stuck on is based on the counting principle.
I have been trying to find a way to output all the possible permutations ( without Replacement) from a varying
number of inputs

Example 1 :
HorseA
HorseB .
............................

HorseA
HorseB ....is one and only permutation ( a 2 X 1 matrix)



Example 2 :
HorseA Horse C
HorseB EMPTY
..................................

HorseA
HorseB

and

HorseC
HorseB ..... are the permutations (2X2 matrix)





Example 3 :

HorseA HorseC
HorseB HorseD
............................................
HorseA
HorseB

and

HorseC
HorseB

and

HorseA
HorseD

and

HorseC
HorseD

.........are the permutations (2X2 matrix)







I have been trying with for loops. But it is more difficult than it seems. I need the loops top output all
permutations. THE FIRST COLUMN IN THE MATRICES MUST ALWAYS BE FULL -- NOT THE CASE HOWEVER FOR THE OTHER COLUMNS

Re: Help with countinig principle
 

Any good links to websites explaining the counting principle? Because I'm not sure I understand it from your explination. Is it simply that you can match ever item in a cell, with every item in every other column except items in the same row as itself?

(i.e. that's why you didn't match A to C in either of your examples, or B to D in the third example)?