document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=412390>Question 412390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.how many ways can 5 people occupy 8 chair if no two people are to occupy the same chair?\r<BR>\n" );
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document.write( "i do not understand why this question have to use permutation instead of combinations. >.<\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #289661 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=289661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> permutations assume that order is important.\r<BR>\n" );
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document.write( "combinations assume that order is not important.\r<BR>\n" );
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document.write( "you have a total of 8 chairs.\r<BR>\n" );
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document.write( "5 people can occupy these chairs in P(8,5) = 8! / 3! = 6720 ways.\r<BR>\n" );
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document.write( "That's a lot of ways.\r<BR>\n" );
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document.write( "To make it simpler to see, let's assume there are 3 chairs and 2 people.\r<BR>\n" );
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document.write( "In how many ways can those 2 people occupy 3 chairs.\r<BR>\n" );
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document.write( "The answer should be 3! / 1! = 6 ways.\r<BR>\n" );
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document.write( "Let's label the chairs a, b, and c.\r<BR>\n" );
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document.write( "Now we draw the possible number of sets of 2 from 3 chairs.\r<BR>\n" );
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document.write( "They would be:\r<BR>\n" );
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document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "ba<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "ca<BR>\n" );
document.write( "cb\r<BR>\n" );
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document.write( "Notice that the 6 possible ways include sets that involve the same people, only in a different order.\r<BR>\n" );
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document.write( "ab can be paired with ba<BR>\n" );
document.write( "ac can be paired with ca<BR>\n" );
document.write( "bc can be paired with cb\r<BR>\n" );
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document.write( "If we were dealing with combinations, then the answer would be 3 possible ways because we only have 3 sets where the people involved in each set are different from the other sets.\r<BR>\n" );
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document.write( "you would have:\r<BR>\n" );
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document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "bc\r<BR>\n" );
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document.write( "Order, in this case, would not be important, so you would have less possible sets.\r<BR>\n" );
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document.write( "None of these sets have the same 2 people in them.\r<BR>\n" );
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document.write( "Formula for permutations is n! / (n-x)!\r<BR>\n" );
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document.write( "Formula for combinations is n! / ((n-x)! * x!)\r<BR>\n" );
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document.write( "With permutations the answer is 3!/1! = 3*2*1/1 = 6\r<BR>\n" );
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document.write( "With combinations the answer is 3!/(1!2!) = 3*2*1/1*2 = 3\r<BR>\n" );
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document.write( "The answer is because, when you arrange people in chairs, order is important.\r<BR>\n" );
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document.write( "If I did my  math correctly, your answer should be 8! / 3! = 6720 possible ways.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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