6Cr⋅6C6−r =6C0⋅6C6+6C1⋅6C5+6C2⋅6C4+ C3⋅6C3+6C4⋅6C2+6C5⋅6C1+6C6⋅6C0 Now, (1+x)6⋅(1+x)6=(6C0+6C1x+6C2x2+ 6C3x3+...+6C6x6)(6C0+6C1x+6C2x2 +6C3x3+...+6C6x6) On comparing the coefficients of x6 from both sides, we have 6C0⋅6C6+6C1⋅6C5+6C2⋅6C4+...+ =