C++ vs Matlab Script for 493 - UNDER THE RAINBOW

void solve()
{
  mpz_class EXPECTATION = 0;
    mpz_class sum = 0;
    for(int i = 2; i <= 7; i++) //Contains the number of balls at each "color #". ie, when i == 2,
                                    //We calculate the probability/expectation for 2 distinct colors
    {
        mpz_class f1;
        mpz_class f2, numerator;
        numerator = nCr(f1, 9*i, 20-i) * nCr(f2, 7, i); // ( 7 C n )* ( 9*n C 20-n )
        cout << "NUMERATOR = " << numerator.get_str() << "\t\t";
        EXPECTATION += (i * numerator); // E(X) = x_i * P(x_i)
        sum += numerator;
        cout << "Done with ... " << i << "\t SUM = " << sum.get_str() << endl;
        cout << "EXPECTATION IS " << EXPECTATION.get_str()<< endl << endl;

    }
    mpf_t num, denom;
    mp_exp_t exponent;

//C++ Formatting Black Magic
    mpf_init(num); mpf_init(denom);
    mpf_set_str(num, EXPECTATION.get_str().c_str(), 10);
    mpf_set_str(denom, sum.get_str().c_str(), 10);
    size_t digits = 20;
    cout << "NUM = " << mpf_get_str(NULL, &exponent, 10, digits, num) << endl;
    cout << "DENOM = " << mpf_get_str(NULL, &exponent, 10, digits, denom) << endl;

    mpf_t result;
    mpf_init(result);
    mpf_div(result, num, denom);
    mpf_class t (result);
//Printing result
    cout << "RESULT IS " << t.get_str(exponent, 10, 0) << endl;
}
//In this case, the "Result" is about 6.055 (which is the wrong answer. I checked by plugging in and getting an intimidating red X mark indicating my folly)

//Compare to this matlab script
%Project Euler - 493 (UNDER THE RAINBOW)
%Given 70 balls in an urn (10 for each of the seven folors in the rainbow)
%What is the expected number of distinct colors in 20 randomly picked
%balls?

%Because this is a monte carlo simulation, it doesnt give an exact answer
%Only a really really good approximation (about 6.382)
clear
close
NUM_TRIALS = 100000
recurringCount = 0
for N = 1:NUM_TRIALS
   URN(1:1, 1:7)= 10;
   Size_Urn = sum(URN);
   for trial = 1:20 %20 trials
       randNum = rand() * Size_Urn +10;
       color = (floor(randNum/10));
       URN(color) = URN(color) - 1;
       Size_Urn = Size_Urn -1;
   end

   distinct_Colors = 0;
   for urnInd = 1:7
       if(URN(urnInd) ~= 10)
           distinct_Colors = distinct_Colors + 1;
       end
   end
   recurringCount = recurringCount + distinct_Colors;
end

format long
recurringCount / NUM_TRIALS