1.排列:
从N个东东中不重复取出M个并作排列,共有几种方法:P=N!/!
例如:从1-5中取出3个数不重复,问能组成几个三位数?
解答:P=5!/!=5!/2!=54321/=543=60
也可以这样想从五个数中取出三个放三个固定位置
那么第一个位置可以放五个数中任一一个,所以有5种可能选法,那么第二个位置余下四个数中任一个,....4.....,那么第三个位置3
所以总共的排列为543=60。
如果可以重复选,总共的排列是555=125
2.组合:
从N个东东中不重复取出M个,共有几种方法:
C=P/P=N!/!/M
C=P/P=5!/2!/3!=543/=10
可以这样理解:组合与排列的区别就在于取出的M个作不作排列-即M的全排列P=M!,
那末他们之间关系就有先做组合再作M的全排列就得到了排列
所以CP=P,由此可得组合公式
性质:C=C, N )
即C=C, 5 )=C = 5!/3!/2!=10
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