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If the coefficients of $x^{7}$ and $x^{8}$ in ${(2 + \frac{x}{3})}^{n}$ are equal, then value of $n$ is

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Correct option is B

Tr+1, the (r+1)th term in the expansion of 2+x3nis given by Tr+1=nCr2n−rx3r=nCr2n−r3rxr According to the given condition nC72n−737=nC82n−838⇒ nC7 nC8=2n−838⋅372n−7⇒ n!7!(n−7)!8!(n−8)!n!=16⇒ 8n−7=16⇒ 48=n−7 ⇒ n=55

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If the coefficients of x7 and x8 in 2+x3nare equal, then value of n is

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If the coefficients of $x^{7}$ and $x^{8}$ in ${(2 + \frac{x}{3})}^{n}$ are equal, then value of $n$ is