binomial calculator

function combination (a, b) {
  return factorial(a) / (factorial(a - b) * factorial(b));
}

function factorial (a) {
  let res = 1;
  while (a) {
     res *= a;
     a--;
  }
  return res;
}

function generalBinomialTerm (total, n, x, y) {
  if (total < n || total < 0 || n < 0 || x < 0 || y < 0 || typeof x !== 'number' || typeof y !== 'number' || typeof x !== 'number' || typeof y !== 'number') return;
  return combination(total, n) * (x ** n) * (y ** (total - n));
}

function binomialSum (from, to, total, x, y) {
  let sum = 0;
  for (let i = from; i <= to; i++) {
    sum += generalBinomialTerm(total, i, x, y);
  }
  return sum;
}

function dice (amount, dice, difficulty, win) {
  return ('D' + dice + ' DIFFICULTY ' + difficulty + ' SKILL LEVEL ' + amount + '= ' + binomialSum(difficulty, amount, amount, win, (1 - win)) + '\n');
}

function dices (list, level, difficulty, win) {
  let probabilities = '';
  lists.forEach(a => { probabilities += dice(level, a, difficulty, win) });
  console.log(probabilities);
}