document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1070897>Question 1070897</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1) 6 books are to be chosen from 8 different books<BR>\n" );
document.write( "(i) Find the number of different selections of 6 books that could be made (ans 28)<BR>\n" );
document.write( "A clock is to be displayed on a shelf with 3 of the 8 different books on each side of it. Find the number of ways this can be done if <BR>\n" );
document.write( "(i) there are no restrictions in the choice of books (ans 20160<BR>\n" );
document.write( "(ii) 3 of the eight books are music books which have to be kept together (ans 720) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #685885 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=685885\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (i) The clock makes no difference.<BR>\n" );
document.write( "You figure out how to choose the 6 books and line them up,<BR>\n" );
document.write( "and then just make a space in the middle of the row of 6 books<BR>\n" );
document.write( "to place the clock There are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2A7%2A6%2A5%2A4%2A3=highlight%2820160%29 ALIGN=MIDDLE  ALT=\"8%2A7%2A6%2A5%2A4%2A3=highlight%2820160%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways to do it,<BR>\n" );
document.write( "permutations of 6 objects taken from a set of 8.<BR>\n" );
document.write( " <BR>\n" );
document.write( "(ii) I interpret that question as meaning that<BR>\n" );
document.write( "you cannot pout only 1 or 2 of the music books on the shelf.<BR>\n" );
document.write( "It is either all or none of them,<BR>\n" );
document.write( "and since excluding those 3 music books leaves us with only<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-3=5 ALIGN=MIDDLE  ALT=\"8-3=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > books, and we need 6,<BR>\n" );
document.write( "the 3 music books go on the shelf in one of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%282%29 ALIGN=MIDDLE  ALT=\"red%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways:<BR>\n" );
document.write( "on the left of the clock, or on the right.<BR>\n" );
document.write( "We still need to figure out in which order<BR>\n" );
document.write( "(from left to right) we line them up.<BR>\n" );
document.write( "That gives us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A2=green%286%29 ALIGN=MIDDLE  ALT=\"3%2A2=green%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > options.<BR>\n" );
document.write( "Then, there are the other 5 books<BR>\n" );
document.write( "for you to decide what to do w it them.<BR>\n" );
document.write( "You need to pick 3, and decide in what order to display them.<BR>\n" );
document.write( "That gives you<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A4%2A3=60 ALIGN=MIDDLE  ALT=\"5%2A4%2A3=60\"   DISABLED_style= \"max-width:90%; height:auto;\" > different options.<BR>\n" );
document.write( "All in all there are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%282%29%2Agreen%286%29%2A60=highlight%28720%29 ALIGN=MIDDLE  ALT=\"red%282%29%2Agreen%286%29%2A60=highlight%28720%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "ways to do it.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );