fact[n_] := 
        If[n > 20, 
          n^(n + 0.5) Sqrt[2 Pi]/Exp[n],  n!];
comb[n_, r_] := N[fact[n]/fact[r]/fact[n - r]];
pr[n_, n1_, r_, k_] := 
      comb[n1, k] comb[n - n1, r - k]/comb[n, r]

n = 26000; r = 1000; k = 2;
n = 26000; r = 1000; k = 3;
n = 26000; r = 10000 ; k = 30 ;
n = 2820000; r = 280000; k = 2;
n = 2820000; r = (292475 + 25 + 2209 + 1); k = 3;
n = 2820000;r = (292475 + 25 + 2209 + 1)*3;k = 
      3*3;

r/3

sol0 = FindMinimum[-pr[n, n1, r, k], {n1, 
              n*k/r}][[2]];
ps = Sum[pr[n, n1, r, k], {n1, 0, 200}];
prl := Sum[pr[n, n1, r, k], {n1, 0, n1l}]/ps
sol1 = FindRoot[prl == 0.975, {n1l, 10, 100}];
sol2 = 
        FindRoot[
          Sum[pr[n, n1, r, k], {n1, 0, n1l}]/ps == 0.025, {n1l, 10, 
            100}];
{sol0, sol2, sol1}

{Sum[pr[n, n1, r, k], {n1, 0, n1l}]/ps /. sol1, 
      Sum[pr[n, n1, r, k], {n1, 0, n1l}]/ps /. sol2}

Sum[pr[n, n1, r, k], {n1, 0, n1l}]/ps /. {n1l -> 27}