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404C4−4C1303C4+4C2202C4−4C3101C4 is equal to

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a

(401)4

b

(101)4

c

0

d

(201)4

answer is B.

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Detailed Solution

The given expression is the coefficient of x4 in 4C0(1+x)404−4C1(1+x)303+4C2(1+x)202−4C3(1+x)101+4C4 = Coefficient of x4 in (1+x)101−14= Coefficient of x4 in 101C1x+101C2x2+⋯4=(101)4

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404C4−4C1303C4+4C2202C4−4C3101C4 is equal to