Binomial TheoremHard

Question

The coefficient of x52 in the expansion(x - 3)100-m. 2m is  :

Options

A.100C47
B.100C48
C.- 100C52
D.- 100C100

Solution

S = (x - 3)100-m 2m
S = 100C0 (x - 3)100 + 100C1 (x - 3)99 . 2 + ...... + 100C100 . 2100
S = (2 + (x -3))100 = (x - 1)100
Co-efficient of x52 = 100C52 = 100C48

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