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