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Coefficient of $x^{17}$ in the polynomial $P (x)$ $= \prod_{r = 0}^{17} (x +^{35} C_{r})$ is

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234

36C17

235−36C17

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Correct option is A

P(x) is a polynomial of degree 18, and coefficient of x17 is N=35C0+35C1+35C2+…+35C17 (1)Using nCr=nCn−r, we can write N as N=35C35+35C34+…+35C18 (2)Adding (1) and (2), we get 2N=35C0+35C1+…+35C35=235⇒ N=234

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Coefficient of x17 in the polynomial P(x)=∏r=017 (x+35Cr) is

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Coefficient of $x^{17}$ in the polynomial $P (x)$ $= \prod_{r = 0}^{17} (x +^{35} C_{r})$ is