If 50c r = 50c r + 2 find r.

By formula, ⁿc_x = ⁿc_y
⇔ x = y or x + y = n
Now, ⁵⁰c_r = ⁵⁰c_{r + 2}
⇒ r + r + 2 = 50 or r = r + 2
⇒ 2r = 48 [∵ r = r + 2 is not possible]
∴ r = 24