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The coefficient of x⁵³ in the expansion $\sum_{m = 0}^{100}^{100} C_{m} (x - 3)^{100 - m} 2^{m}$ is

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100C47

100C53

−100C53

100C100

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Correct option is C

The given sigma is the expansion of [(x−3)+2]100=(x−1)100=(1−x)100Therefore, x53 will occur in T54.T54=100C53(−x)53Therefore, the coefficient is -100C53

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The coefficient of x53 in the expansion ∑m=0100 100Cm(x−3)100−m2m is

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The coefficient of x⁵³ in the expansion $\sum_{m = 0}^{100}^{100} C_{m} (x - 3)^{100 - m} 2^{m}$ is