The number of values of r satisfying the equation  69C3r−1−69Cr2=69Cr2−1−69C3r is

69C3r−1+69C3r=69Cr2−1+69Cr2or    70C3r=70Cr2Thus, r2=3r or 70=3r+r2   r=0,3 or   r= 7,−10Hence, r = 3 and 7 (as the given equation is not defined for r = 0 and -10).