UPSC NDA Math Model Paper 7

⇒ C(47, 4) + C(51, 3) + C(50, 3) + C(49, 3) + C(48, 3) + C(47, 3)
= {C(47, 4) + C(47, 3)} + C(51, 3) + C(50, 3) + C(49, 3) + C(48, 3)
As we know that, C (n, r - 1) + C (n, r) = C (n + 1, r)
⇒ {C(47, 4) + C(47, 3)} + C(51, 3) + C(50, 3) + C(49, 3) + C(48, 3)
= {C (48, 4) + C(48, 3)} + C(51, 3) + C(50, 3) + C(49, 3)
⇒ {C (48, 4) + C(48, 3)} + C(51, 3) + C(50, 3) + C(49, 3) = { C(49, 4) + C(49, 3)} + C(51, 3) + C(50, 3)
⇒ {C(49, 4) + C(49, 3)} + C(51, 3) + C(50, 3) = {C(50, 4) + C(50, 3)} + C(51, 3)
⇒ {C(50, 4) + C(50, 3)} + C(51, 3) = { C(51, 4) + C(51, 3)} = C(52, 4)