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

⁵⁶P_{r + 6} = 56! / [56 - (r + 6) ]! = 56! / (50 - r)!
⁵⁴P_{r + 3} = 54! / [54 - (r + 3) ]! = 54! / (51 - r)!
⁵⁶P_{r + 6} / ⁵⁴P_{r + 3} = [ ( 56! / (50 - r)! ) x ( (51 - r)! / 54!) ]
( 56 x 55 x 54! / (50 - r)! ) x ( (51-r).(50-r)! ) / 54 !
= 56 x 55 x (51-r)

⁵⁶P_{r + 6} / ⁵⁴P_{r + 3} = 30800 / 1
=> 56 x 55 x (51-r) = 30800
=> (51-r) = 10
=> r = 41