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# If ^{35}C_{n+7} = ^{35}C_{4n–2} then find the value of n.

Answer :

Given: ^{35}C_{n+7} = ^{35}C_{4n–2} Need to find: Value of n We know, one of the property of combination is: If ^{n}C_{r} = ^{n}C_{t}, then, (i) r = t OR (ii) r + t = n Applying property (i) we get, ⇒ n + 7 = 4n – 2 ⇒ 3n = 9 ⇒ n = 3 Applying property (ii) we get, ⇒ n + 7 + 4n – 2 = 35 ⇒ 5n = 30 ⇒ n = 6 Therefore, the value of n is either 3 or 6.

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