Permutations And Combinations Question 20

Question: If $ ^{56}{P _{r+6}}{{:}^{54}}{P _{r+3}}=30800:1 $ , then $ r= $ [Roorkee 1983; Kurukshetra CEE 1998]

Options:

A) 31

B) 41

C) 51

D) None of these

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ \frac{56\ !}{(50-r)\ !}\times \frac{(51-r)\ !}{54\ !} $ $ =\frac{30800}{1}\Rightarrow 56\times 55\times (51-r)=30800 $

$ \Rightarrow $ $ r=41 $ .

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