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Question

Determine n if

(i) 2nC3: nC2=12:1 (ii) 2nC3: nC3=11:1

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Solution

(i) Here 2nC3:nC2=12:1

(2n)!3!(2n3)!×2!(n2)!n!=121

(2n)(2n1)(2n2)(2n3)!3×2! (2n3)!×2!(n2)!n(n1)(n2)!=121

(2n)(2n1)(2n2)3×1n(n1)=121

4(2n1)3=121

8n4=36n=5

(ii) Here 2nC3: nC3=11:1

(2n)!3!(2n3)!×2!(n3)!n!=111

(2n)(2n1)(2n2)(2n3)!3! (2n3)!×3!(n3)!n(n1)(n2)(n3)!=111

(2n)(2n1)(2n2)n(n1)(n2)=111

4(2n1)n2=111

8n4=11n22

3n=18n=6.


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