document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197328>Question 1197328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Four people form a line at a grocery store. What is the probability that they line up in descending order of age? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830557 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=830557\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer:  <font color=red>1/24</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Explanation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are 4 people for the first slot, then 3 for the next, and so on until we count down to 1<BR>\n" );
document.write( "4,3,2,1<BR>\n" );
document.write( "Multiply out those items<BR>\n" );
document.write( "4*3*2*1 = 24\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Many calculators have an exclamation mark button, which represents factorials<BR>\n" );
document.write( "4! = 4*3*2*1 = 24<BR>\n" );
document.write( "4! = 24\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This represents the number of ways to line up the four people. Order matters of course.<BR>\n" );
document.write( "Only one way has all four people in the correct order of descending age.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore, we arrive at 1/24 as our answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "An alternative way to calculate the '24' is to follow these steps, through use of the nPr permutation formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n P r = (n!)/( (n-r)! )<BR>\n" );
document.write( "4 P 4 = (4!)/( (4-4)! )<BR>\n" );
document.write( "4 P 4 = (4!)/( 0! )<BR>\n" );
document.write( "4 P 4 = (4*3*2*1)/( 1 )<BR>\n" );
document.write( "4 P 4 = 4*3*2*1<BR>\n" );
document.write( "4 P 4 = 24\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Though as you can probably spot, the factorial of 4! = 4*3*2*1 is part of 4P4. Meaning that we're basically following the same pathway as the previous section.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );