document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=437758>Question 437758</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The man picks 1 from each of the following short stories every night and reads one short story from each of the following catagories: 1 of 5 mysteries, 1 of 4 non-fiction, 1 of 6 teen tales, 1 of 3 Robin Cook books, and and 1 of 5 historical novels. How many options does he have if he must start and end with either a mystery or a teen tale?Can you help with an explanation of how to go about solving a simpler problem too? I am so stuck. I think it is a permutation??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #302840 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=302840\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think it may be simpler than it looks.<BR>\n" );
document.write( "The man could choose from the categories in<BR>\n" );
document.write( "any order he wishes except for the 1st and last night.<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "The problem is hard to interpret. I think they are talking about<BR>\n" );
document.write( "5 successive nights that he reads a single short story.<BR>\n" );
document.write( "I don't think I can go beyond 5 successive nights because<BR>\n" );
document.write( "I don't know how many short stories are in each book.<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "I'll use 1 letter for each category:<BR>\n" );
document.write( "M - 5<BR>\n" );
document.write( "N - 4<BR>\n" );
document.write( "T - 6<BR>\n" );
document.write( "R - 3<BR>\n" );
document.write( "H - 5<BR>\n" );
document.write( "------<BR>\n" );
document.write( "total - 23<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "The 1st night, he chooses between<BR>\n" );
document.write( "M - 5<BR>\n" );
document.write( "T - 6<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "total - 11 ways to choose<BR>\n" );
document.write( "2nd night: there are 23 - 1 = 22 possible ways he can choose<BR>\n" );
document.write( "3rd night:  there are 23 - 2 = 21 possible ways he can choose<BR>\n" );
document.write( "4th night:  there are 23 - 3 = 20 possible ways he can choose<BR>\n" );
document.write( "5th night:  there are 11 - 1 = 10 possible ways he can choose<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "The choices must be multiplied to get all the possible orders<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+11%2A22%2A21%2A21%2A10+=+1016400+ ALIGN=MIDDLE  ALT=\"+11%2A22%2A21%2A21%2A10+=+1016400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are 1,016,400 possible orderings of short stories he can<BR>\n" );
document.write( "read on 5 successive nights<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "You should get a 2nd opinion on this, too. These kind of<BR>\n" );
document.write( "problems can be very tricky, but they are good for the brain.<BR>\n" );
document.write( "   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );