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对于组合数恒等式的证明无固定的方法,使得人们常感到无从下手,下面介绍证明组合恒等式的几种方法,供读者参考.一、构造组合模型例1求证:证明构造组合模型如下:从n个男学生及n个女学生中,选出n个学生组成一个代表团,其中男学生至少有1名,并在其中选择1名男学生为团长,问有多少种不同的选法?选法一按选出的男学生人数k分类,男学生选法有Cnk种,女学生选法有Cnn-k=
There are no fixed methods for the proof of combinatorial number identities, which makes people often feel that there is no way to start. Here are some methods to prove the combinatorial identities for the readers’ reference. First, construct the combinatorial model Case 1 Proof: prove that the constructive combinatorial model is as follows: from n Among the male students and n female students, n students are selected to form a delegation. Among them, there are at least 1 male student, and 1 male student is selected as the head of the group. How many different selection methods are there? According to the number of male students selected by k, there are Cnk male students and Cnn-k female female students.