JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Critical Thinking Questions

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

    A) 31

    B) 41

    C) 51

    D) None of these

    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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