If ⁵⁶P_{r + 6} : ⁵⁴P_{r + 3} = 30800 : 1 then the value of r is?

Question: If ⁵⁶P_{r + 6} : ⁵⁴P_{r + 3} = 30800 : 1 then the value of r is?

Solution:
⁵⁶Pr + 6 : ⁵⁴P_{r + 3} = 30800 : 1
⇒ 56!/(50 - r)! = (30800 × 54!)/(51 - r!)
⇒ 56 × 55 = 30800/(51 - r)
⇒ 51 - r = 10
∴ r = 41