Consider the expression 20Cr20C0+20Cr−120C1+20Cr−220C2+...+20C0⋅20Cr For maximum value of above expression r should be equal to 20 . as 20C20⋅20C0+20C19⋅20C1+...+20C20⋅20C0 =(20C0)2+(20C1)2+...+(20C20)2=40C20 Which is the maximum value of the expression, So, r=20.