document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1152123>Question 1152123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the laboratory analysis of samples from a chemical<BR>\n" );
document.write( "process, five samples from the process are analyzed daily. In<BR>\n" );
document.write( "addition, a control sample is analyzed two times each day to<BR>\n" );
document.write( "check the calibration of the laboratory instruments.\r<BR>\n" );
document.write( "\n" );
document.write( "(a) How  many  different  sequences  of  process  and  control<BR>\n" );
document.write( "samples  are  possible  each  day?  Assume  that  the  five<BR>\n" );
document.write( "process samples are considered identical and that the two<BR>\n" );
document.write( "control samples are considered identical.<BR>\n" );
document.write( "(b) How  many  different  sequences  of  process  and  control<BR>\n" );
document.write( "samples are possible if we consider the five process samples<BR>\n" );
document.write( "to be different and the two control samples to be identical?<BR>\n" );
document.write( "(c) For the same situation as part (b), how many sequences<BR>\n" );
document.write( "are possible if the first test of each day must be a control<BR>\n" );
document.write( "sample?\r<BR>\n" );
document.write( "\n" );
document.write( "a.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%21%2F%282%21%2A5%21%29 ALIGN=MIDDLE  ALT=\"7%21%2F%282%21%2A5%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%21%2F%282%21%29 ALIGN=MIDDLE  ALT=\"7%21%2F%282%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "c. ... It is said to be 6!. But, how's that possible? I need clarification for this </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #774054 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=774054\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Regarding part (c),  because the control samples are considered identical, and the first sample must be a control, that leaves one control and 5 distinct process samples, resulting in 6! possible arrangements.<br>\r<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><BR>\n" );
document.write( "{CC} = control<BR>\n" );
document.write( "{DEFGH} = process\r<BR>\n" );
document.write( "\n" );
document.write( "C { DEFGHC }<BR>\n" );
document.write( "    ^^^^^^<BR>\n" );
document.write( "      6! ways to arrange these </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );