組合數(shù)學(xué)之容斥原理

1、12345|ASAASA 或或.中的補(bǔ)集或余集中的補(bǔ)集或余集在在表示表示其中其中SAA67BABAa )(BABAb )(nnAAAAAAa 2121)(nnAAAAAAb 2121)(8BABABA 9,717500| ,1005500| BA.1475500| BA.1571471100| BABABA10CBACBCABACBACBA niijnnjkkjiniijjiniinAAAAAAAAAAAA12111121) 1(11nnniijjkkjiniijjiniinnAAAAAAAAANAAANAAA 211112121)1(|12.333| ,1666| ,2000|1666 ,

2、5 , 410000| ,8336 , 410000|5005410000| ,2500410000|656565464544AAAAAAAAAAAA456456454656456| 10000(|)|5334AAAAAAAAAAAAAAA1312123111( , )|( 1) |mmiiiiiimiiimf m nAXAAAAAAAA 210(1)( ,2)(2)( ,3)(3)( 1) ()( 1)( , )()nnnmmninimm mC mmC mmmmC m i mi 14 kinikiikCkknS0),()1(!1),(15nkkknkknCknnnnT0)!)(,2(22)

3、1()!1()(02( )2!( 1)(2, )()!2nkknT nnCnk k nknk1617121232211212!|( 1)|nnniiiiiiniiinUAnAAAAAAAA 12 , 1,211niAAAAnii)!(21knAAAkiii18nkknknkknCknnU0)!)(,2(22) 1(),2(22kknCknn1920 !11! 31! 21! 111!nnDnnnAAA 2121)!(|21knAAAkiii 22.!1)1(! 31! 21! 111!)1(! 3! 2! 1! 0),()1()!3)(3 ,()!2)(2 ,()!1)(1 ,(!21 nnn

4、nnnnnnnCnnCnnCnnCnAAADnnnnn2324254224! 4! 6! 5!7!7212121 AAAAAA262728|! 5|4321432143215AAAAAAAAAAAAAAAAAQkjiji 29.53! 1 )4 , 4(! 2)3 , 4(! 3)2 , 4(! 4)1 , 4(! 5|43215 CCCCAAAAQ30! 1 )1, 1()1()!3()3 , 1()!2()2 , 1()!1()1 , 1(!|121 nnCnnCnnCnnCnAAAQnnn31kakaapppn2121 32.1,|., 2 , 1,|khjipppnAAAjikjipp

5、nAAhjihjijiji kkkkkkpppnpppnppnppnpnpnnAAAn111111|)(2121121121 333435 3637 11010010111111103839. 11001, 2100121 rr nkkkxCrCR0)()( 404142;110010011)( CA;1101)(11 CA.110010010)(11 DA;110010011)( CA43442211)1(1000)1(1001xxxxxRxRR 45 .)()()()()(2121 OCACAOCAOOCACA或或46 kiikikCrCrCr021)()()(. )()() )()()(

6、02010021 njjjniiiknkkiikixCrxCrxCrCrCR4723121)1()1 , 1()1(1100)1(1101xxxxxRxxRxRR 2234131)21(101111101101xxxxxxRxRR 48.651)341()31(10110110111001100113222xxxxxxxxRxRR .41061)651()341(10011001110110110011001100132322xxxxxxxxxRxRR 4950 515212121211|! |!(1)!(2)!( 1)1! ( 1)0!nnnnnnnQAAAnAAAnrnrnrr 53545556 54323