document.write( "Question 1044457: nCr:nC(r-1) = 2:3 , nC(r-2):nC(r-1) = 4:3 find n and r\r
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Algebra.Com's Answer #659786 by Edwin McCravy(20055) $\"\"$ $\"About$
You can put this solution on YOUR website!
nCr:nC(r-1) = 2:3 , nC(r-2):nC(r-1) = 4:3 find n and r
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document.write( "Simplify the first equation:\r\n" );
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document.write( "Divide both sides by n!\r\n" );
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document.write( "In the right side, write r! as r(r-1)!\r\n" );
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document.write( "Divide both sides by (r-1)!\r\n" );
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document.write( "Write (n-r+1)! as (n-r+1)(n-r)!\r\n" );
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document.write( "Divide both sides by (n-r)!\r\n" );
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document.write( "Looks better turned around:\r\n" );
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document.write( "nC(r-2):nC(r-1) = 4:3 \r\n" );
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document.write( "Simplify the second equation:\r\n" );
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document.write( "Divide both sides by n!\r\n" );
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document.write( "In the left side, write (r-1)! as (r-1)(r-2)!\r\n" );
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document.write( "Divide both sides by (r-2)!\r\n" );
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document.write( "On the right side, write (n-r+2)! as (n-r+2)(n-r+1)!\r\n" );
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document.write( "Divide both sides by (n-r+1)!\r\n" );
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document.write( "Now we solve the system of two equations for r and n\r\n" );
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document.write( "I'll let you solve that by elimination (addition). \r\n" );
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document.write( "n = 34, r = 21\r\n" );
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document.write( "Checking in the first given proportion:\r\n" );
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document.write( "nCr:nC(r-1) = 2:3 , nCr-2:nCr-1 = 4:3\r\n" );
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document.write( "34C21:34C20 = 927983760:1391975640\r\n" );
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document.write( "Both those huge integers are divisible by the\r\n" );
document.write( "huge integer 463991880\r\n" );
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document.write( "927983760/463991880 = 2 and 1391975640/463991880 = 3\r\n" );
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document.write( "So that checks.\r\n" );
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document.write( "Checking n = 34, r = 21 in the second given proportion:\r\n" );
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document.write( "nC(r-2):nC(r-1) = 4:3\r\n" );
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document.write( "34C19:34C20 = 1855967520:1391975640\r\n" );
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document.write( "Both those huge integers are divisible by the\r\n" );
document.write( "huge integer 463991880\r\n" );
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document.write( "1855967520/463991880 = 4 and from above 1391975640/463991880 = 3\r\n" );
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document.write( "That also checks.\r\n" );
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document.write( "Edwin
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