document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=218176>Question 218176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kindly answer this question please!!! Thanks!!  In how many ways 4 people be seated in a row of 6 chairs if   A.they can be seated anywhere B. the empty chairs are adjacent to each other?                                            </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #164339 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=164339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4 people 6 chairs<BR>\n" );
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document.write( "sitting anywhere, the number is 15.<BR>\n" );
document.write( "if the empty chairs have to be adjacent, the number is 5<BR>\n" );
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document.write( "let's do adjacent first.<BR>\n" );
document.write( "you have 6 chairs and 4 people.<BR>\n" );
document.write( "that means 2 empty chairs.<BR>\n" );
document.write( "if they have to be together, they become equivalent to 1 empty chair with the total number of chairs being 5.<BR>\n" );
document.write( "you now have 5 chairs and one of them has to be empty. <BR>\n" );
document.write( "this can happen in 5 ways.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "effff<BR>\n" );
document.write( "fefff<BR>\n" );
document.write( "ffeff<BR>\n" );
document.write( "fffef<BR>\n" );
document.write( "ffffe<BR>\n" );
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document.write( "no other combination is possible.<BR>\n" );
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document.write( "general formula for number of combinations is:<BR>\n" );
document.write( "n! / ((x)!*(n-x)!)<BR>\n" );
document.write( "formula for this problem is 5! / (1!*4!)<BR>\n" );
document.write( "where:<BR>\n" );
document.write( "1! represents x!<BR>\n" );
document.write( "4! represents (n-x)!<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the first part of your problem is solved as follows:<BR>\n" );
document.write( "you have 6 slots.<BR>\n" );
document.write( "you can fill them with 4 people<BR>\n" );
document.write( "that will leave 2 empty slots.<BR>\n" );
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document.write( "the general formula for number of possible combinations of 4 out of 6 is once again n! / ((x)!*(n-x)!)<BR>\n" );
document.write( "This becomes 6! / (2!*4!)<BR>\n" );
document.write( "where:<BR>\n" );
document.write( "n = 6<BR>\n" );
document.write( "x = 2<BR>\n" );
document.write( "n-x = 4<BR>\n" );
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document.write( "The answer is 6*5*4*3*2*1 / 2*1*4*3*2*1  30/2 = 15<BR>\n" );
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document.write( "there are 15 combinations possible.<BR>\n" );
document.write( "They are:<BR>\n" );
document.write( "eeffff<BR>\n" );
document.write( "efefff<BR>\n" );
document.write( "effeff<BR>\n" );
document.write( "efffef<BR>\n" );
document.write( "effffe<BR>\n" );
document.write( "feefff<BR>\n" );
document.write( "fefeff<BR>\n" );
document.write( "feffef<BR>\n" );
document.write( "fefffe<BR>\n" );
document.write( "ffeeff<BR>\n" );
document.write( "ffefef<BR>\n" );
document.write( "ffeffe<BR>\n" );
document.write( "fffeef<BR>\n" );
document.write( "fffefe<BR>\n" );
document.write( "ffffee<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "You have 15 ways in which you can fill the 6 seats with 4 people assuming they can sit anywhere they want.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "You have 5 ways in which you can fill the 6 seats with 4 people assuming the empty seats have to be together.<BR>\n" );
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document.write( " </SPAN>\n" );
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