If the sum of binomial coefficient in the expansion $(1 + x)^{n}$ is $256$ , then $n$ is

6

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7

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8

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9

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Solution

The correct option is C $8$
$(1 + x)^{n} = C_{0} + C_{1} x + \dots + C_{n} x^{n}$
Sum of coefficients is $C_{0} + C_{1} + \dots + C_{n} = 2^{n} C_{0} + C_{1} + \dots + C_{n} = 256 2^{n} = 256 2^{n} = 2^{8} n = 8$

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