Find string permutations in F#

stringPermutations.fs

let stringPermutations (s : string) = 
    let rec permute result rest =
        match rest with
        | "" -> [result]
        | _ -> 
            rest 
            |> Seq.mapi (fun i -> fun c -> 
                permute (result + c.ToString()) (rest.Remove(i, 1)))
            |> Seq.concat 
            |> Seq.toList
    permute "" s

let testStringPermutationsCount s =
    let factorial n = 
        let rec factorialIter result current = 
            match current with
            | _ when current > n -> result
            | _ -> factorialIter (result * current) (current + 1)
        factorialIter 1 1

    let permutations = Set.ofList (stringPermutations s)
    permutations.Count = factorial s.Length