ll@n,@m,a[n],b[],p[];
rd((a,b,p)(n));
rep(i,n)b[i]<?=a[i];
double d[m+1][1<<n];
d[0][0]=0;
rep(i,1,1<<n){
	d[0][i]=d[0][i&i-1]+1.0/a[__builtin_ctz(i)];
}
rep(j,1,m+1){
	rep(i,1<<n){
		d[j][i]=0;
		rep(k,n){
			if(i&1<<k){
				d[j][i]>?=(d[j][i^1<<k]+1.0/b[k])*(1.0/p[k])+d[j-1][i]*(1.0-1.0/p[k]);
			}
		}
	}
}
wt(d[m][(1<<n)-1]);