Question
Download Solution PDFIf \(\rm 5\times {^nP_4}=7\times {^{(n-1)}P_4}\), then find the value of n
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
\(\rm ^nP_r=\frac{n!}{(n-r)!}={n\times (n-1)\times .....\times (n-r+1)}\)
Calculation:
Given: \(\rm 5\times {^nP_4}=7\times {^{(n-1)}P_4}\)
\(\rm \Rightarrow 5\times n\times (n-1)\times (n-2)\times (n-3)=7\times(n-1)\times (n-2)\times (n-3)\times (n-4) \)
\(\rm \Rightarrow 5\times n=7\times (n-4) \)
\(\rm \Rightarrow 5 n=7n-28 \)
\(\rm \Rightarrow 2n=28 \)
\(\rm \Rightarrow n=14 \)
Hence, option (4) is correct.
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