If 56Pr + 6 : 54Pr + 3 = 30800 : 1 then the value of r is

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