Page 176 - Fixtures

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.[( ) r = n +1 m = n

: 20 ()

∑C (20,k)C (20,k − 1)]
k =1

:( ) C(20,k − 1) = C(20,20 − k + 1)

. 20 (20, k )C (20, k − 1) = 20 − k + 1) = C(40, 21)

∑C ∑C (20,k)C (20,20
k =1 k =1

. 20 C (50, k )C (50 − k, 20 − k ) ()

∑
k=0

C(n,m)C(m,k) = C(n,k)C(n − k,m − k)

.( )k ≤ m ≤ n

20 20

∑C (50,k)C (50 − k,20 − k) = ∑C (50,20)C (20,k)
k=0 k =0
20

∑= C (50, 20) C (20,k) = C(50, 2) × 220
k =0

n−1  C (n,k) 3 4 ( )
  5
∑n + 1)  =
k=0 C (n,k) + C(n,k

.C(n,k) + C(n,k + 1) = C(n + 1,k + 1)