If ^35 C_ n+7 = ^35 C_ 4n-2 , then write the values of n. - Vidyadip

Question

If ${^\text{35}}\text{C}_{\text{n}+7}={^\text{35}}\text{C}_{\text{4n-2}},$ then write the values of n.

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Answer

${^\text{35}}\text{C}_{\text{n}+7}={^\text{35}}\text{C}_{\text{4n-2}}$ ⇒ n + 7 = 4n - 2 ⇒ 3n = 9 ⇒ n = 3 ${^\text{35}}\text{C}_{35-(\text{n}+7})={^\text{35}}\text{C}_{\text{4n-2}}$ ⇒ 35 - (n + 7) = 4x - 2 ⇒ 35 - x - 7 = 4x - 2 ⇒ 5x = 30 ⇒ n = 6

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