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  • Determine n if ^2n C _3 : ^n C _3 = 12 : 1

Q.2.     Determine n if

            (i)\; ^{2n}C_{3}:^{n}C_{3}=12:1

Answers (1)

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Given that : (i)\; ^{2n}C_{3}:^{n}C_{3}=12:1

              \Rightarrow \, \, \frac{^{2n}C_3}{^nC_3}=\frac{12}{1}

The ratio can be written as

   \Rightarrow \, \, \frac{\frac{2n!}{(2n-3)!3!}}{\frac{n!}{(n-3)!3!}}=\frac{12}{1}

 \Rightarrow \, \, {\frac{2n!(n-3)!}{(2n-3)!n!}}=\frac{12}{1}

  \Rightarrow \, \, \frac{2n\times (2n-1)\times (2n-2)\times (2n-3)!\times (n-3)!}{(2n-3)!\times n\times (n-1)\times(n-2)\times (n-3)! }=\frac{12}{1}

\Rightarrow \, \, \frac{2n\times (2n-1)\times (2n-2)}{ n\times (n-1)\times(n-2) }=\frac{12}{1}

\Rightarrow \, \, \frac{2\times (2n-1)\times 2}{ (n-2) }=\frac{12}{1}

\Rightarrow \, \, \frac{4\times (2n-1)}{ (n-2) }=\frac{12}{1}

\Rightarrow \, \, \frac{ (2n-1)}{ (n-2) }=\frac{3}{1}

\Rightarrow \, \, 2n-1=3n-6

\Rightarrow \, \, 6-1=3n-2n

\Rightarrow \, \, n=5

 

 

 

 

 

Posted by

seema garhwal

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