(*
There are exactly ten ways of selecting three from five, 12345:

123, 124, 125, 134, 135, 145, 234, 235, 245, and 345

In combinatorics, we use the notation, ^(5)C_(3) = 10.

In general,
^(n)C_(r) = 	
n!

r!(n?r)!
	,where r ? n, n! = n×(n?1)×...×3×2×1, and 0! = 1.

It is not until n = 23, that a value exceeds one-million: ^(23)C_(10) = 1144066.

How many, not necessarily distinct, values of  ^(n)C_(r), for 1 ? n ? 100, are greater than one-million?
*)

open Big_int;;

let bmill = big_int_of_int 1000000;;

(* n!/(r!*(n-r!)) *)
let comb r n =
  let rec fact i n =
    if(i>n) then (big_int_of_int 1) else
    mult_int_big_int i (fact (i+1) n)
  in
    div_big_int (fact (r+1) n) (fact 2 (n-r))
;;

let rec search r n =
  if(n>100) then 0 else
  if(r>n) then (search 0 (n+1)) else

  ( if (gt_big_int (comb r n) bmill) then 1 else 0 )
  +(search (r+1) n)
;;

Printf.printf "%d\n" (search 0 0);;