string combinatorics, generate nCr strings from n strings

The best way is to make a function that finds all string combinations of length N and use that recursively.
Then you just call it for each length.

  
ArrayList FindAllStrings(string input)
{
  ArrayList strings;

  for(int i = 0; i<=input.Length(); i++)
  AddStrings(strings, input, i, "");
}

AddStrings(ArrayList strings, string input, int N, string leading = "")
{
  if(N == 0)
    strings.Add(leading);
  else
  {
    for(int i = 0; i + N < input.Length(); i++)
      addStrings(strings, input.SubString(i+1), N-1, leading + input[i]);
  }

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If you want the commas, change line 18 to
AddStrings(strings, input.Substring(i + 1), N - 1, leading + (leading.Length > 0 ? ",":"") + input[ i]);

Use the libaray here written by Adrian Akison:
http://www.codeproject.com/KB/recipes/Combinatorics.aspx

Simple Demo: Idle-Mind-502573.flv

Click on Project --> Add Reference --> Browse --> Facet.Combinatorics.dll

Then you want to use the Variations class like this:

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Windows.Forms;

namespace WindowsFormsApplication1
{
    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }

        private void button1_Click(object sender, EventArgs e)
        {
            listBox1.DataSource = Variations(textBox1.Text);
        }

        private List<string> Variations(string input)
        {
            List<string> values = new List<string>();
            for (int i=0; i < input.Length; i++)
            {
                values.Add(input.Substring(i,1));
            }

            List<string> results = new List<string>();
            for (int i = input.Length; i >= 1; i--)
            {
                Facet.Combinatorics.Variations<string> vars = new Facet.Combinatorics.Variations<string>(values.AsReadOnly(), i);
                foreach (IList<string> set in vars)
                {
                    results.Add(String.Join(",", set));
                }
            }
            return results;
        }
    }
}

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Here's the output:

a,b,c,d
a,b,d,c
a,c,b,d
a,d,b,c
a,c,d,b
a,d,c,b
b,a,c,d
b,a,d,c
c,a,b,d
d,a,b,c
c,a,d,b
d,a,c,b
b,c,a,d
b,d,a,c
c,b,a,d
d,b,a,c
c,d,a,b
d,c,a,b
b,c,d,a
b,d,c,a
c,b,d,a
d,b,c,a
c,d,b,a
d,c,b,a
a,b,c
a,b,d
a,c,b
a,d,b
a,c,d
a,d,c
b,a,c
b,a,d
c,a,b
d,a,b
c,a,d
d,a,c
b,c,a
b,d,a
c,b,a
d,b,a
c,d,a
d,c,a
b,c,d
b,d,c
c,b,d
d,b,c
c,d,b
d,c,b
a,b
a,c
a,d
b,a
c,a
d,a
b,c
b,d
c,b
d,b
c,d
d,c
a
b
c
d

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Idle_Mind, that does all the possible permutations of all the possible combinations. It's also using another library and even then, the code looks just about as long as mine.

TrialUser, I assume your inclusion of both a,b and b,a was accidental and you just wanted the combinations. To do all permutations in mine you would just change
input.Substring(i + 1)
to
input.Substring(0,i) + input.Substring(i + 1)

You do need to make sure to have
using System.Collections
at the top to use the ArrayList or you could modify the code to use whatever collection type you prefer.

The library can also do Permuations and Combinations as well...it's pretty flexible.

Just last week I was solving a Permutation problem on ProjectEuler.net and came across this website. http://www.bearcave.com/random_hacks/permute.html

In particular, I found this graphic interesting, http://www.bearcave.com/random_hacks/permute_diagram.jpg

Merely implementing that, with an otter loop that iterates through removing letters solves it.