//-----------------------------------------------------------------
// Dinner Lottery  ( P = 2 )
// Author:  Ana Paula Tomas
// November 2016
//-----------------------------------------------------------------


#include <stdio.h>
#include <stdlib.h>

#define DEBUG

// P cannot change
#define P 2

// problem bounds
#define NMAX 50
#define KMAX 10
#define DRAWSIZE 10


#define MIN(X,Y) ((X) < (Y)? (X):(Y))
#define MAX(X,Y) ((X) > (Y)? (X):(Y))


int N, K, Draw;
double Time[KMAX+1][KMAX+1][KMAX+1];
double Comb[NMAX+1][DRAWSIZE+1];   // KMAX and DRAWSIZE same value

void init_comb() {
  int i,j, r = MAX(Draw,K);
  Comb[0][0]=1;
  for(i=0; i<N;i++){
    Comb[i+1][0]=1;
    for(j=1; j<= r && j<=i;j++)
      Comb[i+1][j] = Comb[i][j-1] + Comb[i][j];
    if (i+1<= r) Comb[i+1][i+1] = 1;
  }
}

void init_time() {
  int a, b, c;

  for(b=0; b<=K; b++) 
    Time[0][0][b] = Time[0][b][0] = 0;
  for(a=1; a<=K; a++)
    for(b=1; b<=a; b++)
      Time[0][a][b]= Time[0][b][a] = -1;

  for(c=1;c <= K;c++) {
    for(a=0; a<=K; a++)
      for(b=0; b<=a; b++)
	Time[c][a][b]= Time[c][b][a] = -1;
  }
}

double find_time(int c,int a, int b)
{ 
  int sc,sa,sb,sr;
  double p, p0, total = 0;

  if (Time[c][a][b] >= 0) return Time[c][a][b];
 
  Time[c][a][b] = 0;
  p0 = 0;
  for(sc=MAX(0,Draw-(N-c)); sc <= MIN(c,Draw); sc++)
    for(sa=MAX(0,(Draw-sc)-(N-c-a)); sa <= MIN(a,Draw-sc); sa++)
      for(sb=MAX(0,(Draw-sc-sa)-(N-c-a-b)); sb <= MIN(b,Draw-sc-sa); sb++) {
	sr = Draw-sc-sa-sb;
	if (sc==0 && sa==0 && sb ==0) 
	  p = p0 = Comb[N-a-b-c][sr];
	else {
	  p = Comb[c][sc]*Comb[a][sa]*Comb[b][sb]*Comb[N-a-b-c][sr];
	  Time[c][a][b]  += p*find_time(c-sc,a-sa,b-sb);
	}
	total += p;
      }
  
  Time[c][a][b] += total;
  Time[c][a][b] /= (total-p0);
  Time[c][b][a] = Time[c][a][b];
  return Time[c][a][b];

}

int main() {

  int k,  i, c;
  int bet[NMAX+1]={0};

  scanf("%d%d%d",&N,&Draw,&K);

  c = 0;
  for(k=0;k<K;k++){
    scanf("%d",&i);
    bet[i] = 1;
  }

  for(k=0;k<K;k++){
    scanf("%d",&i);
    bet[i]++;
    if (bet[i] == 2) c++;
  }

  init_time();
  init_comb();

  printf("%.8lf\n",find_time(c,K-c,K-c));

  return 0;
}