document.write( "Question 1175056: Please help me to solve this Qeustion(1) Prove that nCr=n+1Cr-nCr-1
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Algebra.Com's Answer #800580 by math_helper(2461) $\"\"$ $\"About$

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document.write( "1) nCr = n!/((n-r)!r!)   <<< this is what we need to show for the RHS\r
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document.write( "  RHS: C(n+1,r) - C(n,r-1)   where C(a,b) = \"aCb\"
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document.write( " = \r
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document.write( "Factor out n+1 from the first term, and multiply the 2nd term by r/r:
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document.write( " = \r
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document.write( "Notice (n+1-r)! ( = (n-(r-1))! ) is the same as  (n+1-r)(n-r)!\r
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document.write( " = \r
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document.write( "Factor out  n!/((n-r)!r!) and re-write:\r
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document.write( " = \r
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document.write( "= \r
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document.write( "= \r
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document.write( "=   ■\r
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document.write( "---------\r
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document.write( "(2) nPr = n!/(n-r)! = P(n,r)  <<< P(x,y) notation used below\r
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document.write( "    (n-r+1)*P(n,r-1)  \r
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document.write( "=    \r
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document.write( "=    \r
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document.write( "=    \r
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document.write( "=      ■\r
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