document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118511>Question 1118511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a)using the digits 2,3,4,5,6,7<BR>\n" );
document.write( "(I) how many three number digit numbers can be formed if repetition is not permitted?<BR>\n" );
document.write( "(ii) how many of these 3-digit numbers would be odd?<BR>\n" );
document.write( "(iii)how many of these 3-digit numbers would be divisible by 5?<BR>\n" );
document.write( "(c) find the term containing x^9 in the expansion of (x^3 - 2/x)^15 without actually doing the expansion  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733883 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=733883\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(aI) 6*5*4 = 120  (6 choices for first digit; 5 for second; 4 for third)<br><BR>\n" );
document.write( "(aII) 3*5*4 = 60  (only 3 choices for last digit, because it must be odd; then 5 for second and 4 for third)<br><BR>\n" );
document.write( "(aIII) 1*5*4 = 20  (only 1 choice for last digit, because the number has to be divisible by 5; then 5 for second and 4 for third)<br><BR>\n" );
document.write( "(c) When expanding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-2%2Fx%29%5E15 ALIGN=MIDDLE  ALT=\"x%5E3-2%2Fx%29%5E15\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get a term with x^9, you need to take the x^3 term 6 times and the 2/x term 9 times:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3%29%5E6%2A%28x%5E-1%29%5E9+=+%28x%5E18%29%28x%5E-9%29+=+x%5E9%29 ALIGN=MIDDLE  ALT=\"%28x%5E3%29%5E6%2A%28x%5E-1%29%5E9+=+%28x%5E18%29%28x%5E-9%29+=+x%5E9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The term is then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2815%2C6%29%28%28x%5E3%29%5E6%29%28-2%2Fx%29%5E9+=+%285005%29%28-512%29x%5E9+=+-2562560x%5E9 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );