Page 181 - Fixtures

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()

C(25, 8)C(15, 0) + C(25, 7)C(15,1) + + C(25, 0)C(15, 8)

C(41,7) ( ) C(41, 8) ( ) C(40,7) ( ) C(40, 8) ( )

k ( )
0 () )
∑ (−1)iC (n,i)C(n − i,k − i)
i=0 )

2n−2 ( ) 2n−1 ( ) 2n ( ) )
)
2≤k ≤n (

: C(n,k) + 2C(n,k − 1) + C(n,k − 2)

C(3n,k) ( ) C(n + 1,k) ( )

C(n + 2,k − 1) ( ) C(n + 2,k) ( )

[C(n,1)]2 + 2[C(n,2)]2 + + n[C(n,n)]2 (

n2C(2n,n) ( ) nC(2n,n) ( )

n C(2n,n) ( ) C (3n, n) ,n n C(2n,n) ( )
3( )
2 5( ) 3

: y (
7()
2 ()
(xy − 2y−3)16
[MAΘ 1991] (

16C(16,6)( ) 8C(16, 6) ( ) 16C(16, 4) ( ) 8C(16, 4) ( )

x2 b a [AIME 2000 I] ( )

670 ( ) : a + b (ax + b)2000 x3

669 ( ) 668 ( ) 667 ( )