choosin.js

function fact(n) {
  var res = 1
  for (var i = 1; i <= n; i++) {
    res *= i
  }
  return res
}

function choose(n, k) {

  return fact(n)/(fact(k) * fact(n - k))

}

// out of n distinguishable choices, we have a subset of k elements
// this returns the probability of getting at least one of the k elements when choosing groups of j
function probWantedSubset(n, k, j) {
  var res = 0
  for (var i = 0; i < Math.min(j, k); i++) {
    res += choose(k, j-i)*choose(n-k, i)
  }
  res /= choose(n, k)
  return res
}