mathjs/lib/function/probability/combinations.js

module.exports = function (math) {
  var util = require('../../util/index'),

      BigNumber = require('bignumber.js'),
      collection = require('../../type/collection'),

      isNumber = util.number.isNumber,
      isInteger = util.number.isInteger;

  /**
   * Compute the number of combinations of n items taken k at a time
   *
   *     combinations(n, k)
   *
   * combinations only takes integer arguments
   * the following condition must be enforced: k <= n
   *
   * @Param {Number} n
   * @Param {Number} k
   * @return {Number} combinations
   */
  math.combinations = function combinations (n, k) {
    var arity = arguments.length;
    if (arity != 2) {
      throw new math.error.ArgumentsError('combinations', arguments.length, 2);
    }

    if (isNumber(n)) {
      if (!isInteger(n) || n < 0) {
        throw new TypeError('Positive integer value enpected in function combinations');
      }
      if (k > n) {
        throw new TypeError('k must be less than or equal to n');
      }
      return Math.floor(math.factorial(n) / (math.factorial(k) * math.factorial(n-k)));
    }

    var isPositiveInteger = function(x) {
      if (!x.round().equals(x) || x.lt(0)) {
        return false;
      }
      return true;
    };

    if (n instanceof BigNumber) {
        // make sure k is a BigNumber as well
        k = new BigNumber(k);
        if (isPositiveInteger(n) && isPositiveInteger(k)) {
          return math.floor(math.divide(math.factorial(n),
                      math.multiply(math.factorial(k),
                          math.factorial(math.subtract(n, k)))));
        }
        else {
          throw new TypeError('Positive integer value expected in function permutations');
        }
    }

    throw new math.error.UnsupportedTypeError('combinations', n);
  };
};