Page 118 - Fixtures

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C(15 − n, 2)×C (n, 2) = (15 − n)×(14 − n) × n ×(n − 1)
22

= (15 − n)(n − 1) × (14 − n) ×n
22

= 49 − (n − 8)2 × 49 − (n − 7)2
22

.n = 8 n = 7

.C(8,2)×C(7,2) = 28 ×21 = 588
[MAΘ 2011] ( )

a + b + 2c = 35

z = c −1 y =b −1 x = a −1

z . x + y + 2z = 31
. 0,1,2, 3,…,15

. x + y = 31, x + y = 29, …, x + y = 1

C(32,1) + C(30,1) + C(28,1) + + C(2,1)

= 32 + 30 + 28 + + 2 = 272

y = b −1 x = a −1 :

. x + y + 2z = 31 z =c−1

. yx

y = 2r x = 2t + 1 .