Page 170 - Fixtures

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[AIME 2000 II] ( )

1+1+1+1+1
2!!× 17 ! 3 !!×16 ! 4 !!×15 ! 6 !!× 13! 7 !!× 12!

+ 1 + 1 =N
8 !!× 11! 9 !!× 10 ! 1!!× 18 !
N
100

19 !

C(19,2) + C(19, 3) + + C(19, 8) + C(19,9) = 19N

19

C(19,n) = C(19,19 − n) ∑ C (19,n) = 219
n=0

∑, . 9 C (19,n) = 219 = 218

n=0 2

.19N = 218 −C(19,1) −C(19, 0) = 218 − 19 − 1 = 262124

137 . N = 137.96 N = 262124 = 13796

100 19

.N

100

10 i [MAΘ 1992] ( )

∑ ∑C(i,k)

i=1 k =1

. i = C (i,1) + C (i,2) + + C (i,i) = 2i − 1

∑C (i,k)
k =1