document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=887579>Question 887579</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in how many ways can nine people be seated on a bench if only three seats are available </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536765 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=536765\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this should be 9P3 = 9*8*7 = 504\r<BR>\n" );
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document.write( "make it simpler and you can see how it works.\r<BR>\n" );
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document.write( "assume 4 people for 3 seats.\r<BR>\n" );
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document.write( "number of ways would be 4P3 = 4*3*2 = 24\r<BR>\n" );
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document.write( "let the people be a,b,c,d\r<BR>\n" );
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document.write( "number of possible combinations where order doesn't matter would be 4C3 = 4.\r<BR>\n" );
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document.write( "those combinations are:\r<BR>\n" );
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document.write( "abc<BR>\n" );
document.write( "abd<BR>\n" );
document.write( "acd<BR>\n" );
document.write( "bcd\r<BR>\n" );
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document.write( "each one of these combinations can be arranged in 6 ways.\r<BR>\n" );
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document.write( "abc arrangements would be:\r<BR>\n" );
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document.write( "abc<BR>\n" );
document.write( "acb<BR>\n" );
document.write( "bac<BR>\n" );
document.write( "bca<BR>\n" );
document.write( "cab<BR>\n" );
document.write( "cba\r<BR>\n" );
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document.write( "abd arrangements would be:\r<BR>\n" );
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document.write( "abd<BR>\n" );
document.write( "adb<BR>\n" );
document.write( "bad<BR>\n" );
document.write( "bda<BR>\n" );
document.write( "dab<BR>\n" );
document.write( "dba\r<BR>\n" );
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document.write( "acd arrangements would be:\r<BR>\n" );
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document.write( "acd<BR>\n" );
document.write( "adc<BR>\n" );
document.write( "cad<BR>\n" );
document.write( "cda<BR>\n" );
document.write( "dac<BR>\n" );
document.write( "dca\r<BR>\n" );
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document.write( "bcd arrangements would be:\r<BR>\n" );
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document.write( "bcd<BR>\n" );
document.write( "bdc<BR>\n" );
document.write( "cbd<BR>\n" );
document.write( "cdb<BR>\n" );
document.write( "dbc<BR>\n" );
document.write( "dcb \r<BR>\n" );
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document.write( "total possible arrangements are 4 * 6 = 24\r<BR>\n" );
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document.write( "the formula to use is 4P3 in this example.\r<BR>\n" );
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document.write( "note that 4P3 = 4C3 * 3! which means you got 4 possible combinations * 6 possible arrangements for each combination to get 24 possible permutations.\r<BR>\n" );
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document.write( "the same permutation formula is applied when n = 9 to get 9P3 which is equal to 504.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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