document.write( "Question 989699: If C(n,3)=C(n,4),then the value of n?????please help me to solve this problem. \n" ); document.write( "

Algebra.Com's Answer #609934 by macston(5194) $\"\"$ $\"About$

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\n" ); document.write( "C(n,3)=n!/(3!(n-3)!)
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\n" ); document.write( "C(n,4)=n!/(4!(n-4)!)
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\n" ); document.write( "n!/(3!(n-3)!)=n!/(4!(n-4)!) Divide each side by n!
\n" ); document.write( "1/(3!(n-3)!)=1/(4!(n-4)!) Cross multiply
\n" ); document.write( "3!(n-3)!=4!(n-4)! Divide each side by 3!
\n" ); document.write( "(n-3)!=4(n-4)! Divide each side by (n-4)!*(Note below)
\n" ); document.write( "n-3=4(1)
\n" ); document.write( "n-3=4
\n" ); document.write( "n=7
\n" ); document.write( "ANSWER: n=7
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\n" ); document.write( "*NOTE: (n-3)!=(n-3)(n-4)! so (n-3)!/(n-4)!=(n-3)
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\n" ); document.write( "CHECK:
\n" ); document.write( "n!/(3!(n-3)!)=n!/(4!(n-4)!)=
\n" ); document.write( "7!/(3!(7-3!))=7!/(4!(7-4)!)=
\n" ); document.write( "7!/(3!4!)=7!/(4!3!)
\n" ); document.write( "(7*6*5)/(3*2*1)=(7*6*5)/(3*2*1)
\n" ); document.write( "210/6=210/6
\n" ); document.write( "35=35\r
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