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If the ratio \ \ ^(2n)C3 .\ \ ^n C3 is e...

If the ratio `\ \ ^(2n)C_3` .`\ \ ^n C_3` is equal to 11:1 find `ndot`

Text Solution

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We have,
`.^(2n)C_(3): .^(n)C_(3)=11:1`
or `(.(2n)C_(3))/(.^(n)C_(3))=(11)/(1)`
or `(((2n)!)/((2n-3)!(3!)))/((n!)/((n-3)!(3!)))=(11)/(1)`
or `((2n)!)/((2n-3)!)xx((n-3)!)/(n!)=(11)/(1)`
or `((2n)(2n-1)(2n-2))/(n(n-1)(n-2))=(11)/(1)`
or `(4(2n-1))/(n-2)=(11)/(1)`
or 8n-4=11n-22
or 3n=18 or n=6
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