Combinations and permutations in Javascript. Demo at http://jsbin.com/xufomalori/edit?js,console

combinatorics.js

// Combinations and permutations.
// Counts can be verified at http://www.calculatorsoup.com/calculators/discretemathematics/permutations.php
// noprotect

var combinations = function(arr) {
  var result = [];
  
  for (var i=0; i<arr.length; i++) {
    var item1 = arr[i];
    
    for (var j=i+1; j<arr.length; j++) {
      var item2 = arr[j];
      
      result.push([item1, item2]);
    }
  }
  
  return result;
}

var permutations = function(arr) {
  var result = [];
  
  for (var i=0; i<arr.length; i++) {
    var item1 = arr[i];
    
    for (var j=0; j<arr.length; j++) {
      var item2 = arr[j];
      
      if (item1 !== item2) {
        result.push([item1, item2]);
      }
    }
  }
  
  return result;  
}

var combinationsn = function(arr, n) {
  var result = [];

  var indexes = [];
  for (var i=0; i<n; i++) {
      indexes.push(i);
  }
  
  var i=0;
  while (i < arr.length) {
    var items = [];
    
    for (var j=0; j<indexes.length; j++) {
      var index = indexes[j];
      items.push(arr[index]);
    }

    var idx = indexes.length - 1;
    var lastIndex = indexes[idx];
    while (lastIndex == arr.length - 1 && idx > 0) {
      idx--;
      lastIndex = indexes[idx];
    }
    
    if (indexes[idx] < arr.length - 1) {
      indexes[idx]++;

      var count = 0;
      for (var k=idx + 1; k<indexes.length; k++) {
        indexes[k] = indexes[idx + count] + 1;
        if (indexes[k] >= arr.length) {
          indexes[k] = arr.length - 1;
        }
        count++;
      }

      i = 0;
    }

    var skip = false;
    for (var k=0; k<items.length - 1; k++) {
      for (var l=k+1; l<items.length; l++) {
        if (items[k] === items[l]) {
          skip = true;
          break;
        }
      }
    }

    if (n == 1) {
      for (var k=0; k<result.length; k++) {
        if (result[k][0] === items[0]) {
          skip = true;
          break;
        }
      }
    }

    if (!skip) {
      result.push(items);
    }
    
    i++;
  }

  return result;
}

var permutationsn = function(arr, n) {
  var result = [];

  var indexes = [];
  for (var i=0; i<n; i++) {
      indexes.push(i);
  }
  
  var i=0;
  while (i < arr.length) {
    var items = [];
    
    for (var j=0; j<indexes.length; j++) {
      var index = indexes[j];
      items.push(arr[index]);
    }

    var idx = indexes.length - 1;
    var lastIndex = indexes[idx];
    while (lastIndex == arr.length - 1 && idx > 0) {
      idx--;
      lastIndex = indexes[idx];
    }
    
    if (indexes[idx] < arr.length - 1) {
      indexes[idx]++;

      for (var k=idx + 1; k<indexes.length; k++) {
        indexes[k] = 0;
      }

      i = 0;
    }

    var skip = false;
    for (var k=0; k<items.length - 1; k++) {
      for (var l=k+1; l<items.length; l++) {
        if (items[k] === items[l]) {
          skip = true;
          break;
        }
      }
    }

    if (n == 1) {
      for (var k=0; k<result.length; k++) {
        if (result[k][0] === items[0]) {
          skip = true;
          break;
        }
      }
    }

    if (!skip) {
      result.push(items);
    }
    
    i++;
  }

  return result;
}

var factorial = function(n) {
  var result = 1;

  for (var i=n; i>0; i--) {
    result *= i;
  }

  return result;
}

var combinationCount = function(n, k) {
  var result = 1;

  var divisor = (factorial(k) * factorial(n - k));
  if (divisor) {
    result = factorial(n) / divisor;
  }

  return result;
}

var permutationCount = function(n, k) {
  var result = 1;

  var divisor = factorial(n - k);
  if (divisor) {
    result = factorial(n) / divisor;
  }

  return result;
}

var list = ['x','y','a','b','c','d','e','f'];
var c = combinations(list);
console.log(c.length + ' combinations.');
console.log(c);

var p = permutations(list);
console.log(p.length + ' permutations.');
console.log(p);

for (var i=1; i<=list.length; i++) {
  console.log(combinationsn(list, i).length == combinationCount(list.length, i));
}

for (var i=1; i<=list.length; i++) {
  console.log(permutationsn(list, i).length == permutationCount(list.length, i));
}