Question:
Find n if n-1P3: nP3 = 1: 9.
Find n if n-1P3: nP3 = 1: 9.
Updated On: Feb 19, 2025
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Solution and Explanation
n-1P3: nP3 = 1: 9
\(⇒\frac{^{n-1}P_3}{^nP_3} = \frac{1}{ 9}\)
\(⇒\frac{\left[\frac{(n-1)!}{(n-1-3)!}\right]}{\left[\frac{n!}{(n-4)!}\right]}=\frac{1}{9}\)
\(⇒\frac{(n-1)!}{(n-4)!}\times\frac{(n-4)!}{n!}=\frac{1}{9}\)
\(⇒\frac{(n-1)!}{n\times(n-1)!}=\frac{1}{9}\)
\(⇒\frac{1}{n}=\frac{1}{9}\)
\(∴n=9\)
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