How many ways to pick XX balls

// See https://math.stackexchange.com/questions/835031/how-many-ways-to-pick-x-balls

double choose_n_balls(int n, int num_types, int *count_per_type)
{
    int total_count = 0;
    for (int i = 0; i < num_types; i++) {
        total_count += count_per_type[i];
    }
    if (n > total_count)
        return 0;
    if (num_types == 1)
        return 1;
    double retval = 0;
    for (int i = 0; i <= count_per_type[0] && i <= n; i++) {
        int new_n = n - i;
        int new_num_types = num_types - 1;
        int new_count_per_type[100] = {0};
        memcpy(new_count_per_type, &(count_per_type[1]), sizeof(count_per_type[0]) * 99);
        retval += choose_n_balls(new_n, new_num_types, new_count_per_type);
    }
    return retval;
}

There is a hard-coded 100 in there. Watch out.