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The coefficient of $x^{2} y^{3}$ in the expansion of $(1 - x + y)^{20}$ is

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20!2!3!

−20!2!3!

20!5!2!3!

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Correct option is D

The general term in the expansion of (1−x+y)20is 20!r!s!t!1r(−x)s(y)t, where r + s + t = 20For x2y3, we have the term 20!15!2!3!115(−x)2(y)3Hence, the coefficient of x2y3 is 20!15!2!3!

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The coefficient of x2y3in the expansion of (1−x+y)20is

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The coefficient of $x^{2} y^{3}$ in the expansion of $(1 - x + y)^{20}$ is