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

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Permutation and Combination

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