For the following, we will presume that since you are sampling without replacement and trying only measure the number of items from your desired group in the sample, then the space of X will include R = {0, 1, ..., r} assuming \(n_1 \ge r\) and \(n-n_1 \ge r\text{.}\) In the case when r is too large for either of these, the formulas below will follow noting that binomial coefficients are zero if the top is smaller than the bottom or if the bottom is negative.