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Question

The coefficient of x10 in (1+x2−x3)8 is

A
476
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B
496
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C
506
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D
528
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Solution

The correct option is D 476
In (1+x2x3)8
There are only two possible ways of x10
Those are (x2)5(13)(x3)0 and (x2)2(x3)2)14
Hence the corresponding coefficients will be
8!5!(3!) and 8!2!(2!)4!
Thus the coefficient of x10 in the above expression is
8!5!(3!)+8!2!(2!)4!
=56+420
=476

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