document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251091>Question 251091</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5 people (A,B,C,D,E)sit together in a theater.  How many ways can they be arranged if personB is seated to the right of, but not necessarily next to, personC???<BR>\n" );
document.write( "How would you figure this out???? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184199 by </B><A HREF=/tutors/aboutme.mpl?userid=palanisamy><B>palanisamy(496)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=palanisamy><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=184199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5 people (A,B,C,D,E)sit together in a theater. <BR>\n" );
document.write( "Total number of arrangements = 5P5 = 5! <BR>\n" );
document.write( "First let us consider the case in which C occupies the left extreme seat.<BR>\n" );
document.write( "The other four people can be arranged in 4P4 = 4!= 1x2x3x4 = 24 ways.\r<BR>\n" );
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document.write( " Next, let C occupy the second seat.<BR>\n" );
document.write( "Excluding B, the first seat can be filled by either one of A,D,E in 3 ways and the other 3 seats can be filled in 3! ways.<BR>\n" );
document.write( "So, total number of ways = 3x3! = 3x3x2x1 = 18\r<BR>\n" );
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document.write( " Next,let C occupy the third seat.<BR>\n" );
document.write( "Excluding B, the first two seats can be filled by either one of A,D,E in <BR>\n" );
document.write( "3P2 = 6 ways and the other 2 seats can be filled in 2! ways.<BR>\n" );
document.write( "So, total number of ways = 6x2! = 6x2x1 = 12\r<BR>\n" );
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document.write( " Next,let C occupy the fourth seat.<BR>\n" );
document.write( "Excluding B, the first three seats can be filled by either one of A,D,E in <BR>\n" );
document.write( "3P3 = 3! ways and the other last seat can be filled by B in 1 way <BR>\n" );
document.write( "So, total number of ways = 3!x1 =3x2x1x1 = 6\r<BR>\n" );
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document.write( "So the total number of ways in which B sits right of C is = 24+18+12+6 =60 \r<BR>\n" );
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document.write( "ANOTHER METHOD<BR>\n" );
document.write( "5 people (A,B,C,D,E)sit together in a theater. <BR>\n" );
document.write( "Total number of arrangements = 5P5 = 5! <BR>\n" );
document.write( "There are only two possible ways.<BR>\n" );
document.write( "Either B can sit to the right of C or B can sit to the left of C.<BR>\n" );
document.write( "The number of ways are equal in both cases.<BR>\n" );
document.write( "Therefore the total number of ways in which B sits right of C is = 5! / 2<BR>\n" );
document.write( "                                                                                                                             =1*2*3*4*5/2  =60                           </SPAN>\n" );
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