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一 分类法解含有特殊元素(位置)的排列组合问题 例1 今有卡片9张,分别写上0,1,2,3,4,5,6,7,8九个数字,现从中任取3张,并排组成三位整数,其中,写6的卡片也可以作为9使用,总共能组成多少个不同的三位偶数. 点拨:数字0不能作首位,含6与不含9,含9不含6,这些都成为分类的因素. 解:(元素优先)按特殊元素6来分类. 第一类,6当6使用,按0划分类别: (1)0在个位有A82(个); (2)0不在个位有A41A71A17(个). 第二类,6当9使用且含有9的三位偶数,按0划
A classification method solves the problem of the arrangement and combination of special elements (positions). Example 1 There are nine cards today, which are written with 0, 1, 2, 3, 4, 5, 6, 7, 8 and nine numbers. 3, side by side to form a three-digit integer, in which the card of 6 can also be used as 9 to form a total of how many different three even numbers. The dial: the number 0 can not be the first place, with 6 and 9 without, with 9 no Including 6, these have become the factors of classification. Solution: (element priority) is classified according to the special element 6. The first type, 6 when 6 is used, divided by 0 categories: (1) 0 has A82 (one) in one place; (2) 0 does not have A41A71A17(s) in place. The second type, 6 when 9 is used and contains the three even numbers of 9, 0