The coefficient of x2y3 in the expansion of (1−x+y)20 is

The general term in the expansion of (1−x+y)20 is20!r!s!t!1r(−x)s(y)t, where r+s+t=20For x2y3, r=15,s=1,t=3we have the term20!15!2!3!115(−x)2(y)3Hence, the coefficient of x2y3 is20!15!2!3!