Given
69C3r−1− 69Cr2= 69Cr2−1− 69C3r⇒ 69C3r−1+ 69C3r= 69Cr2+ 69Cr2−1⇒ 70C3r= 70Cr2⇒3r=r2 or 3r+r2=70⇒r=0,3 or r2+3r−70=0⇒r=0,3 or (r+10)(r−7)=0⇒r=0,3,−10,7
As 3r−1,r2,r2−1,3r∈W and less than or equal to 69, so the required values are
r=3,7
Hence, the number of values of r is 2.