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在解排列组合题时,常遇到有限条件的应用题,我们把被限制的元素称为特殊元素,被限制的位置称为特殊位置.解题时,若优先安排一般元素(或位置),后安排特殊元素(或位置),往往能较快地解决问题.例1.用0到9这十个数字,可以组成多少个没有重复数字的三位数?(课本P.235.例5 )分析:从0到9这十个数中任取三个数字的排列数为P_(10)~3,其中以0为排头的排列数为P_9~2,因此,所求的三位数的个数是:P_(10)~2- P_9~2=648(个)
When we solve the problem of arranging combinatorial problems, we often encounter problems with finite conditions. We call the restricted elements special elements, and the restricted positions are called special positions. When solving problems, if we prioritize general elements (or positions), After arranging special elements (or positions), the problem can often be solved quickly. Example 1. Using a ten-digit number from 0 to 9, how many three-digit numbers can be formed without repeating numbers? (Textbook P.235. Example 5) Analysis: The number of any three numbers from 0 to 9 is P_(10)~3, where the number of zeros is P_9~2, so the three-digit number The number is: P_(10)~2- P_9~2=648 (one)