module _53

let combinationGt1M =
    let f =
        [|0..100|] |> Array.map (fun n -> bigint n) |> Array.map common.factorialI

    let combinations (n, r) =
        f.[n] /  ( f.[r] * f.[n - r] )
        
    [100..-1..0]
    |> Seq.sumBy (fun n ->
        seq { 1 .. n }
        |> Seq.filter (fun r -> combinations (n,r) > 1000000I )
        |> Seq.length
    )