### choose =====================================================================

Tags
----
scripting, JS, internal, treenode, general concept

Parameters
----------
n,k

General description
-------------------

Returns the number of combinations of n items taken k at a time.

For example, the number of five card hands is choose(52,5)

```
                          n!
      choose(n,k) = -------------
                     k! (n - k)!
```
###


Eval_choose = ->
  push(cadr(p1))
  Eval()
  push(caddr(p1))
  Eval()
  choose()

# Result vanishes for k < 0 or k > n. (A=B, p. 19)

#define N p1
#define K p2

choose = ->
  save()

  p2 = pop()
  p1 = pop()

  if (choose_check_args() == 0)
    push_integer(0)
    restore()
    return

  push(p1)
  factorial()

  push(p2)
  factorial()

  divide()

  push(p1)
  push(p2)
  subtract()
  factorial()

  divide()

  restore()

choose_check_args = ->
  if (isNumericAtom(p1) && lessp(p1, zero))
    return 0
  else if (isNumericAtom(p2) && lessp(p2, zero))
    return 0
  else if (isNumericAtom(p1) && isNumericAtom(p2) && lessp(p1, p2))
    return 0
  else
    return 1