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  • Find n if ^n-1 P _3 : ^n P_ 4 = 1 : 9

    Q.9.    Find n if   ^{n-1}P_{3}:^{n}P_{4}=1:9.

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best_answer

Given : ^{n-1}P_{3}:^{n}P_{4}=1:9.

To find the value of n

^{n-1}P_{3}:^{n}P_{4}=1:9.

\Rightarrow \frac{^{n-1}P_3}{^nP_4}=\frac{1}{9}

\Rightarrow \, \, \frac{\frac{(n-1)!}{(n-1-3)!}}{\frac{n!}{n-4!}}=\frac{1}{9}

\Rightarrow \, \, \frac{\frac{(n-1)!}{(n-4)!}}{\frac{n!}{(n-4)!}}=\frac{1}{9}

\Rightarrow \, \, \frac{(n-1)!}{n!}=\frac{1}{9}

\Rightarrow \, \, \frac{(n-1)!}{(n-1)!\times n}=\frac{1}{9}

\Rightarrow \, \, \frac{1}{ n}=\frac{1}{9}

\Rightarrow \, \, n=9.

 

 

 

 

 

 

 

 

 

 

Posted by

seema garhwal

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