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



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

A. 40

B. 41

C. 42

D. None of these

Answer : B. 41


Explanation :

    56Pr + 6 = 56! / [56 - (r + 6) ]! = 56! / (50 - r)!
    54Pr + 3 = 54! / [54 - (r + 3) ]! = 54! / (51 - r)!
    56Pr + 6 / 54Pr + 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)

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


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