›—20 œ‘—œ‘ 1.2

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  1. 1. 20 1: 1.2:
  2. 2. . . 0. 1. 1. 2. 2. 1. 2 , 20, 1.2: 1. 2. 3. 4. 5. . 1. 2. 3. 4. . 1. 2. 3.
  3. 3. . 3 , 20, 1.2: (-)
  4. 4. . ( n). 4 , 20, 1.2: n, 1 n: 12...)2()1(! = nnnn : 0!=1 12...)2()1(! = nnnn 1, 1 1 ,)!1( ! = > = n nnn n
  5. 5. . P(n,k) C(n,k) 5 , 20, 1.2: P(n,k), n! (n-k)! n0 0kn: )1...()2()1( )!( ! ),( += = knnnn kn n knP C(n,k) n! k!(n-k)! n0 0kn To C(n,k) : : )!(! ! ),( knk n knC = k n )!(! ! knk n k n =
  6. 6. . : 6 , 20, 1.2: 1: : = kn n k n knk 2: : + = 1 11 k n k n k n
  7. 7. . () . : . 7 , 20, 1.2: . , , - . , . ( 1.2) ( 1.3) ( 1.4) .
  8. 8. . 1. k () n . : , . 8 , 20, 1.2: , . 4 () ( ) , . (.. 1-2 2-1 )
  9. 9. . 1. : 9 , 20, 1.2: ( 49 6), ( 52 5), . . .
  10. 10. . 1. , : k n 10 , 20, 1.2: k n k n + k kn 1 : ( .. ) ( .. {1,2,..,6} )
  11. 11. . 1. 1. 11 , 20, 1.2: : 1. 2. n ( ). 3. k , ( ( ) : = k n knC ),( , , ..
  12. 12. . 1. 2. 12 , 20, 1.2: : 1. 2. n ( ). 3. k ( ( ) : + =+ k kn kknC 1 ),1( , .. . , .
  13. 13. . 2. 1. 13 , 20, 1.2: 49 6 . ; : : 49 816.983.13... 6 49 == : 1. ( 1, 8, 44, 12, 19, 23 .. 1, 12, 44, 8, 19, 23) 2. 49 6 3. .
  14. 14. . 2. 2. 14 , 20, 1.2: (=) . ; : : 21 67!567!7!77126 = = === = + 21 2!5!2!5!2)!27(!222 == = = = = : 1. ( 1,2 2,1) 2. n=6 ( 1,2,3,4,5,6) k=2 . 3. (.. 1 2 )
  15. 15. . 2. 3. 15 , 20, 1.2: ; (: ,1,2,3,4,5 6 ) : : : 28 2 78 !6!2 !678 !6!2 !8 )!28(!2 !8 2 8 2 127 = = = = = = + : 1. ( 2,5 5,2) 2. 7 ( 0,1,2,3,4,5,6) 2 . 3. (.. 1 2 )
  16. 16. . 2. 4. 16 , 20, 1.2: 5 . : : 52 960.598.2... 5 52 == : 1. 2. n=52 k=5 . 3. .
  17. 17. . 2. 5. 17 , 20, 1.2: 2 {1,2,3,4,5,6,7,8} : : 28... 8 == 28... 2 == : 1. ( ) 2. n=8 ( ) k=2 . 3. .
  18. 18. . 2. 5. (1. ) 18 , 20, 1.2: SOS : k=0,1,2,,n : nnniinn i n ba n n ba n ba n ba i n ba ++ + = =+ = 0110 0 ... 10 )( k n : : i ba n bababa i ba ++ + = =+ = 0 ... 10 )( 32233021120333 0 3 33 3 3 2 3 1 3 0 33 )( babbaabababababa i ba ii i +++= + + + = =+ = niinn i n x n n x n x n x n x i n x ++ + + = =+ = ... 210 1)1( 210 0 ++ + + = =+ = n nnnn i n iinn i n ... 210 11)11( 0 n n nnnn 2... 210 = ++ + +
  19. 19. . 2. 5. (2. ) 19 , 20, 1.2: ={1,2,3,4} : ------------------------------------> C(4,0)=1 ---------------------> C(4,1)=4 ---> C(4,2)=6 },4,3{},4,2{},3,2{},4,1{},3,1{},2,1{ },4{},3{},2{},1{ , {)( =AP ---> C(4,2)=6 --------> C(4,3)=4 --------------------------------> C(4,4)=1 : : } }4,3,2,1{ },4,3,2{},4,3,1{},4,2,1{},3,2,1{ },4,3{},4,2{},3,2{},4,1{},3,1{},2,1{ 4 2 4 4 3 4 2 4 1 4 0 4 = + + + + n n nnnn 2... 210 = ++ + +
  20. 20. . 1. 20 , 20, 1.2: : : ) (= ). . ) . .. 5 , 4 6 , 3 ) . . . : 50 . 5 : 1 . . 1 .
  21. 21. . 2. 21 , 20, 1.2: : : . . : 5 , 5 5 . 4 . : n=3(1 , 1 1 ) k=4. : C(n+k-1,k)=C(3+4-1,4)=C(6,4)=15 .
  22. 22. . 2. 22 , 20, 1.2: : . . : 5 , 5 2 . 4 . : : 0 : C(2+4-1,4)=C(5,4) 1 . 3 C(2+3-1,3)=C(4,3) 2 . 2 C(2+2-1,2)=C(3,2) . : C(5,4)+C(4,3)+C(3,2)=5+4+3=12
  23. 23. . 3. 23 , 20, 1.2: : . - . , . . : 20 3 , 1 6, 2 9 3 5 . ; : 1 C(20,6) 2 C(14,9) 3 C(5,5) : C(20,6)C(14,9)C(5,5) ! , . .
  24. 24. . 4. 24 , 20, 1.2: : . , : : 5 , 5 5 . 4 2 : : 2 : C(2+2-1,2)=C(3,2)=3 3 . C(2+1-1,1)=C(2,1)=2 4 . 1 3+2+1=6 () .
  25. 25. . 1 : 25 , 20, 1.2: = = = = = !4) !3) !2) !1) !0) E D C B A = = = = !7) !6) !5) !4) H G F E
  26. 26. . 2 : 26 , 20, 1.2: = = = = = )2,4() )1,4() )0,4() )2,5() )3,5() CE CD CC PB PA = = = = )3,10() )4,4() )3,4() )2,4() CH CG CF CE
  27. 27. . 3 : 27 , 20, 1.2: = kn n k n
  28. 28. . 1 A={1,2,3,4,5,6,7,8,9,10} 1. A 5 2. A 3 7 28 , 20, 1.2: 5 10 2. A 3 7 3. A 4 6 4. 210