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Determine n if (i) ^2n C2:^n C2=12 :1 ...

Determine n if (i) `^2n C_2:^n C_2=12 :1` (ii) `^2n C_3:^n C_3=11 :1`

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`.^(2n)C_(3): .^(n)C_(2) = 12:1`
`rArr ((2n)!)/(3!(2n-3)!) : (n!)/(2!(n-2)) = 12:1`
`rArr ((2n)(2n-1)(2n-1))/(6): (n(n-1))/(2) = 12:1`
`rArr ((2n)(2n-1)(2n-2))/(6) xx (2)/(n(n-1)) = (12)/(1)`
`rArr (2(2n-1).2)/(3) = 12`
`rArr 2n - 1 = 9`
`rArr n = 5`.
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Determine n if ( i )^(2n)C_(2):^(n)C_(2)=12:1 (ii) ^2nC_(3):^(n)C_(3)=11:1

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(i) If ""^(2n)C_(3) : ""^(n)C_(3)= 11 : 1 , find n. (ii) If ""^(2n)C_(3) : ""^(n)C_(2) = 12 : 1 , find n.