Solving permutation/combination example with MATLAB
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Hi all,
I would like to write a MATLAB function to model a problem:
There are eight boxes, each box containing 8 balls labeled 1 to 8. If I draw one ball from each box, what are all possible combinations of 8 balls for each trial?
One easy combination (out of many) is: 1 1 1 1 1 1 1 1 What is the total number of combinations and what are the sequence of numbers for each?
Extending this idea one step further, what if I draw two balls from each box? One random example would be: [1 2] [2 3] [4 5] [7 8] [7 2] [3 6] [3 9] [3 5]
What if drawing three balls, four balls, etc. from each run?
For the limiting case of drawing 8 balls, the total number of combination is one. [1 2 3 4 5 6 7 8] [1 2 3 4 5 6 7 8] ....... [1 2 3 4 5 6 7 8]
Any help/hint on how this can be implemented efficiently in MATLAB? Thank you.
采纳的回答
Jos (10584)
2014-2-15
0 个投票
hints
(1) start with 1 box with M balls, drawing n balls from it. This will give you the set S(n). Take a look at NCHOOSEK
(2) when drawing from K boxes, you can treat these boxes independently. To obtain all possible combinations of K sets you have to obtain the cartesian product of these K sets S(n). Take a look at ALLCOMB ( you can download here: <http://www.mathworks.com/matlabcentral/fileexchange/10064-allcomb> )
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