let rec permutations xs =
  match xs with
  | [] -> [[]]
  | _ ->
    List.fold_left (fun acc x ->
      let rest = List.filter (fun y -> y <> x) xs in
      let subs = permutations rest in
      acc @ List.map (fun p -> x :: p) subs
    ) [] xs

;;

let ps = permutations [1; 2; 3; 4] in
let count = ref 0 in
List.iter (fun p ->
  match p with
  | [a; _; _; b] when a < b -> count := !count + 1
  | _ -> ()
) ps;
!count