关于组合恒等式,在中学教学中一般是采用二项式的工具证明的。现在的中学教材,在排列组合、二项式紧后的内容是概率,如用概率的想法来证明组合恒等式将是有意思的,而且一般还比较简单。如在教学中给学生以介绍则是很有益的。本文介绍常用的五个重要组合恒等式的概率法。 1.C_n~r=C_(n-1)~r+C_(n-1)~(r-1)(1≤r≤n) 证:从装有大小相同的一个红球余为白球的n个球的口袋中任意摸出r个球,设摸到红球的事件为A,则有: P(A)=C_(n-1)~(r-1)+C_n~r;P(?)=C_(n-1)~r+C_n~r. Regarding the combination of identities, it is generally proved by the binomial tool in the middle school teaching. In the current middle school textbooks, the content of the permutation and binomial is the probability. It would be interesting to prove the combination identity with the idea of ​​probability, and it is generally relatively simple. It is useful to give students an introduction in teaching. This article describes the commonly used five important combinatorial identity probabilities. 1.C_n~r=C_(n-1)~r+C_(n-1)~(r-1)(1≤r≤n) Proof: From a red ball with the same size to a white ball In the pocket of a ball, r balls are arbitrarily drawn. If the event of touching the red ball is A, there are: P(A)=C_(n-1)~(r-1)+C_n~r;P(? )=C_(n-1)~r+C_n~r.