infoarena

 Problema se poate rezolva si folosind prgramarea dinamica. 
Se construieste matricea Ai,j cu semnificatia suma tuturor produselor de j
 factori alesi din primele i numere. Recurenta se poate calcula usor Ai,j=Ai-1,j+Ai-1,j-1*Pi. 
Probabilitatea ceruta va fi An,k impartita la Cn,k (combinari de n luate cate k). 

Program dezastru;
Var f:text;
    i,k,n,p,nn,nk,kk:longint;
    s,pp:real;
    c:array[1..8000] of byte;
    a:array[1..8000] of real;
Begin
  assign(f,'dezastru.in');
  reset(f);
  readln(f,n,k);
  nn:=1;
  for i:=1 to n do begin nn:=nn*i; read(f,a[i]); end;
  nk:=1;
  for i:=1 to n-k do nk:=nk*i;
  s:=0.0;
  pp:=1.0;
  kk:=1;
  for i:=1 to k do begin kk:=kk*i; c[i]:=i; pp:=pp*a[c[i]]; end;
  s:=s+(pp/(nn div nk))*kk;
  if k<>n then
  repeat
   c[k]:=c[k]+1;
   if c[k]=n+1 then
     begin
      p:=k-1;
      while (p>0) and (c[p]=n-k+p) do p:=p-1;
      c[p]:=c[p]+1;
      for i:=p+1 to k do c[i]:=c[i-1]+1;
     end;
    pp:=1.0;
    for i:=1 to k do pp:=pp*a[c[i]];
    s:=s+(pp/(nn div nk))*kk;
  until(c[1]=n-k+1);
  close(f);
  assign(f,'dezastru.out');
  rewrite(f);
  Writeln(f,s:0:6);
  close(f);
End.

3 2
0.3 0.5 0.8

A[0][0]=1;
A[1][1]=0.3; A[1][0]=1;
A[2][2]=0.15; A[2][1]=0.8; A[2][0]=1;
A[3][3]=0.12; A[3][2]=0.79; A[3][1]=1.6; A[3][0]=1

 printf("%.3lf", c);