document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149532>Question 1149532</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Of the seven-letter words that can be formed without repetition from the letters of the word INCLUDE <BR>\n" );
document.write( "how many have the letters N and D separated by more than two letters? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770885 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</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=770885\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I will assume this question is from the same student that asked the number of words when the letters N and D are separated by EXACTLY two letters....<br><BR>\n" );
document.write( "Then, continuing in the same manner as in my response to that question....<br><BR>\n" );
document.write( "(1) N and D separated by THREE letters: (3)(2)(120) = 720<BR>\n" );
document.write( "(2) N and D separated by FOUR letters: (2)(2)(120) = 480<BR>\n" );
document.write( "(3) N and D separated by FIVE letters (the maximum): (1)(2)(120) = 240<br><BR>\n" );
document.write( "ANSWER: 1440<br><BR>\n" );
document.write( "Notice we can see that this method of counting the numbers of words with different numbers of letters between N and D is valid by finding the numbers of words for ALL the possible distances between N and D and showing that the sum is 7! =5040.<br><BR>\n" );
document.write( "N and D separated by ONE letter: (5)(2)(120) = 1200<BR>\n" );
document.write( "N and D separated by ZERO letters: (6)(2)(120) = 1440<br><BR>\n" );
document.write( "That, together with the above response for this question and the earlier response for the case with 2 letters between N and D, gives us:<br><PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "0 letters between: 1440\r\n" );
document.write( "1 letter between:  1200\r\n" );
document.write( "2 letters between:  960\r\n" );
document.write( "3 letters between:  720\r\n" );
document.write( "4 letters between:  480\r\n" );
document.write( "5 letters between:  240\r\n" );
document.write( "         --------------\r\n" );
document.write( "           total   5040</PRE><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );