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Ex 6.4, 2 Determine n if 2nC3 : nC3 = 12 : 1 Let first calculate 2nC3 and nC3 separately 2nC3 = 2 !/3!(2 3)! = ((2 )(2 1)(2 2)(2 3)!)/((3 2 1)(2 3)!) = 2 (2 1)(2 2)/6 Given 2nC3 : nC3 = 12 : 1 2 (2 1)(2 2)/6 : ( 1)( 2)/6 = 12 : 1 2 (2 1)(2 2)/6 : ( 1)( 2)/6 = 12 : 1 ((2 (2 1)(2 2))/6)/( ( 1)( 2)/6) = 12 2n(2n 1)(2n 2)/6 6/( ( 1)( 2)) = 12 2n(2n 1)(2n 2)/( ( 1)( 2)) 6/6 = 12 (2(2n 1). 2(n 1))/(( 1)( 2)) = 12 4(2n 1)(n 1)/(( 1)( 2)) = 12 4(2n 1)/(( 2)) = 12 4(2n 1) = 12(n 2) 8n 4 = 12n 24 4 + 24 = 12n 8n 20 = 4n 20/4 = n 5 = n Thus, n = 5

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo