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Determine n if <br> (i) .^(2n)...

# Determine n if <br> (i) .^(2n)C_(3) : .^(n)C_(3) = 12:1 <br> (ii) .^(2n)C_(3): .^(n)C_(3)= 11:1

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Updated On: 5-8-2020

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Text Solution

Solution :
(i) .^(2n)C_(3):^(n)C_(2) = 12:1 <br> rArr ((2n)!)/(3!(2n-3)!): (n!)/(2!(n-2)!) = 12:1 <br> rArr ((2n).(2n-1)(2n-2))/(6): (n(n-1))/(2) = 12:1 <br> rArr ((2n)(2n-1)(2n-2))/(6) xx (2)/(n(n-1)) = (12)/(1) <br> rArr (2(2n-1).2)/(3) 12 <br> rArr 2n - 1 =9 <br> rArr n = 5 <br> (ii) .^(2n)C_(3):^(n)C_(3) = 11:1 <br> rArr .^(2n)C_(3)xx1 = 11 xx .^(n)C_(3) <br> rArr (2n(2n-1)(2n-2))/(3xx 2xx1) = 11 xx (n(m-1)(n-2))/(3 xx 2xx 1) <br> rArr (2n(2n-1).2(n-1))/(6) xx (6)/(n(n-1)(n-2) = 11 <br> rArr (4(2n-1))/(n-2) =11 <br> rArr 8 n - 4 = 11 n - 22 <br> rArr 22 - 4 = 11n - 8n <br> rArr 18 = 3n rArr n = 6.

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