The hypergeometric distribution (3.22) can be written in various ways. The nine factorials can be organized into binomial coefficients also as follows:

超几何分布(3.22)可以写为多种方式.九个阶乘可以组织成二项式系数，如下：

But the symmetry under exchange of M and n is still not evident; to see it we must write out (3.22) or (3.73) in full, displaying all the individual factorials.

但是M和n交换时的对称性仍然不明显; 要看到它，我们必须完整地写出（3.22）或（3.73），显示所有每个阶乘项。

We may also rewrite (3.22), as an aid to memory, in a more symmetric form: the probability for drawing exactly r red balls and w white ones in n = r + w draws, from an urn containing R red and W white, is

我们也可以用更加对称的形式重写（3.22）,以便帮助记忆：从有R个红球和W个白球的盒中，在n=r+w次抽取中,正好取出r个红球和w个白球的概率是

and in this form it is easily generalized. Suppose that, instead of only two colors, there are k different colors of balls in the urn, $N_1$ of color 1, $N_2$ of color 2, …​ , $N_k$ of color k. The probability for drawing $r_1$ balls of color 1, $r_2$ of color 2, …​ , $r_k$ of color k in $n = \sum r_i$ draws is, as the reader may verify, the generalized hypergeometric distribution:

在这种形式下，它很容易推广。假设，盒子中的球不只有两种颜色，而有k种不同颜色，$N_1$个颜色1的，$N_2$个颜色2的，…​，$N_k$个颜色k的。在$n=\sum r_i$次抽取中,取出了$r_1$个颜色1的球，$r_2$个颜色2的球，…​，$r_k$个颜色k的球的概率是，读者也很容易来验证，广义超几何分布：