document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194573>Question 1194573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In how many ways can 4 people be seated in a row of 12 chairs​ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826805 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=826805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let's say the four people have the code names of A,B,C,D\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We'll have twelve slips of paper with the numbers 1,2,3,...,10,11,12​ written on them (one number per paper). <BR>\n" );
document.write( "Each number refers to a different chair.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The process is that each person will pick a slip of paper at random out of a hat.<BR>\n" );
document.write( "Whatever is chosen is not put back or replaced. In other words, repeats are not allowed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "One possible permutation is: 12,8,7,1<BR>\n" );
document.write( "This means:<BR>\n" );
document.write( "person A is in chair 12<BR>\n" );
document.write( "person B is in chair 8<BR>\n" );
document.write( "person C is in chair 7<BR>\n" );
document.write( "person D is in chair 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "As you can see, we have n = 12 slips of paper to pick from and r = 4 slots to fill. The order matters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That means you'll compute nPr = 12P4 as shown below.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n P r = (n!)/( (n-r)! )<BR>\n" );
document.write( "12 P 4 = (12!)/( (12-4)! )<BR>\n" );
document.write( "12 P 4 = (12!)/( 8! )<BR>\n" );
document.write( "12 P 4 = (12*11*10*9*8!)/( 8! )<BR>\n" );
document.write( "12 P 4 = 12*11*10*9<BR>\n" );
document.write( "12 P 4 = 11880\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "or slightly alternatively<BR>\n" );
document.write( "n P r = (n!)/( (n-r)! )<BR>\n" );
document.write( "12 P 4 = (12!)/( (12-4)! )<BR>\n" );
document.write( "12 P 4 = (12!)/( 8! )<BR>\n" );
document.write( "12 P 4 = (12*11*10*9*8*7*6*5*4*3*2*1)/( 8*7*6*5*4*3*2*1 )<BR>\n" );
document.write( "12 P 4 = (479,001,600)/( 40,320 )<BR>\n" );
document.write( "12 P 4 = 11880\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <font color=red>11880</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );