Page 156 - Fixtures
P. 156
@ @QTQ@ @æa@paˆ@pþàbÉà@ @
= n(n − 1)(n − 2) (n − k + 1)(n − k)!
(k − 1)!(n − k)!
= n(n − 1)(n − 2) (n − k + 1)
(k − 1)!
= n(n − 1)! = nC (n − 1,k − 1)
(k − 1)!(n − k)!
[Hockey Stick Identity]
0≤k ≤n nk
C(k,k) + C(k + 1,k) + + C(n,k) = C(n + 1,k + 1)
k +1
:
. . A = {1,2, 3,…,n + 1}
k +1
.C (n, k ) 1A k +1
{2, 3,…,n + 1} k
2 A k +1
.C(n − 1,k) {3, 4,…,n + 1} k
A k +1 C (k, k ) .
, . n −k
A k +1
.
:
