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Coefficient of x^(8) in (1+x)^(10) + x(1...

Coefficient of `x^(8)` in `(1+x)^(10) + x(1+x)^(9) + x^(2)(1+x)^(8) + ………….x^(9)(1+x) + x^(10)` is

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The correct Answer is:
A
`""^(10)C_(8) + ""^(9)C_(8) + …… +""^(4)C_(2) + ""^(3)C_(1) + ""^(2)C_(0)`
`=""^(4)C_(1) + ""^(4)C_(2) +…….+ ""^(10)C_(8)`
`=""^(11)C_(8) = (11 xx 10 xx 9)/(3 xx 2) = 17=165`
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