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You can put this solution on YOUR website!
\n" ); document.write( "Interesting problem....
\n" ); document.write( "But you didn't state the equation correctly. The equation you show has many counterexamples.
\n" ); document.write( "For n=6 and r=3, the formula says
\n" ); document.write( "7P3 = 6P3+4*6P2. But
\n" ); document.write( "7P3 = 7*6*5 = 210
\n" ); document.write( "6P3 = 6*5*4 = 120
\n" ); document.write( "6P2 = 6*5 = 30
\n" ); document.write( "and
\n" ); document.write( "210 = 120 + 4*30
\n" ); document.write( "is not true.
\n" ); document.write( "The interesting problem is when the formula is stated correctly:
\n" ); document.write( "(n+1)Pr = nPr + r*nP(r-1)
\n" ); document.write( "This is easy to prove algebraically, although the nomenclature is ugly....
\n" ); document.write( "(n+1)Pr = (n+1)(n)(n-1)(n-2)...(n-(r-2)) = (n+1)(n)(n-1)(n-2)...(n-r+2)
\n" ); document.write( "nPr = (n)(n-1)(n-2)...(n-(r-2))(n-(r-1)) = (n)(n-1)(n-2)...(n-r+2)(n-r+1)
\n" ); document.write( "nP(r-1) = (n)(n-1)(n-2)...(n-(r-2)) = (n)(n-1)(n-2)...(n-r+2)
\n" ); document.write( "Then
\n" ); document.write( "nPr + r*nP(r-1) =
\n" ); document.write( "[(n)(n-1)(n-2)...(n-r+2)](n-r+1) + r[(n)(n-1)(n-2)...(n-r+2)] =
\n" ); document.write( "[(n)(n-1)(n-2)...(n-r+2)][(n-r+1)+r] =
\n" ); document.write( "[(n)(n-1)(n-2)...(n-r+2)](n+1)=
\n" ); document.write( "(n+1)(n)(n-1)(n-2)...(n-r+2)
\n" ); document.write( "(n+1)Pr \n" ); document.write( "