number_combos.js

var choices = ['1', '2', '3'],
  combos = [],
  _ = require('underscore');

var addLetter = function(word) {
  var combos = [];
  choices.forEach(function(choice) {
    combos.push(word + choice);
  });
  return combos;
};

combos = addLetter('');

for(i=0; i < 5; i++) {
  combos = combos.map(addLetter);
  combos = _.flatten(combos);
}

combos = combos.filter(function(combo) {
  return combo.indexOf('1') != -1 && combo.indexOf('2') != -1 && combo.indexOf('3') != -1
});

console.log('combos:', combos);
console.log('count:', combos.length);