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试题1(江苏卷,第13题)今有2个红球、3个黄球、4个白球,同色球不加以区分,将这9个球排成一列有种不同的方法(用数字作答).试题特点:本题是一个含有重复元素的排列问题,着力考查分步计数原理、排列组合的基本知识,由于出现了同色球,在排列的基础上增加了对组合原理的考查.思路分析:思路1:因同色球不加以区分,实际上是一个组合问题,共有 C_9~4·C_5~2·C_3~3=1260种不同的方法.思路2:可将9个球进行全排列,然后再将同色球的顺序抵消掉,共有 A_9~9/2!3!4!=1260种不同的方法.方法小结:分步计数原理是本题考查的重要知识
Question 1 (Jiangsu Volume, Question 13) There are two red balls, three yellow balls and four white balls. There is no distinction between the same color ball. There are different ways to put these 9 balls in one row (with numbers) Test questions features: This question is a sequence of elements with repeated elements, focus on examining the principle of step-counting, the basic knowledge of the combination of the combination, due to the emergence of the same color ball, on the basis of the array to increase the combination of the principle of thinking. 1: Because of the same color of the ball does not distinguish between, is actually a combination of problems, a total of C_9 ~ 4 · C_5 ~ 2 · C_3 ~ 3 = 1260 different ways of thinking 2: Nine balls can be arranged in full, and then The order of the same color ball offset, there are A9 ~ 9/2! 3! 4! = 1260 kinds of different methods. Method summary: The principle of step counting is the important knowledge