document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1152347>Question 1152347</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a)How many ways can 10 questions on a test be arranged?\r<BR>\n" );
document.write( "\n" );
document.write( "b)How many ways can 10 questions be arranged on a test, if the easiest and the most difficult questions are side by side?\r<BR>\n" );
document.write( "\n" );
document.write( "c)How many ways can 10 questions on a test be arranged, if the easiest and the most difficult questions are NOT side by side? ( hint: indirect method)\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #774357 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=774357\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\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;\">\r\n" );
document.write( "\r\n" );
document.write( "(a)  10! = 10*9*8*7*6*5*4*3*2*1 = 3628800 ways.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Any of 10 questions can be placed first;\r\n" );
document.write( "\r\n" );
document.write( "     any of remaining 9 questions can be placed 2-nd;\r\n" );
document.write( "\r\n" );
document.write( "     any of remaining 8 questions can be placed 3-rd\r\n" );
document.write( "\r\n" );
document.write( "         . . . . and so on . . . . \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b)  We can consider two special questions as one single object in 2 states, that are its internal permutations AB and BA.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Then we have 9 objects and 9! their permutations with one the special object which has 2 states.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Therefore, in all, there are  2*9! different ways = 725760 ways.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(c)  From the entire set of all possible permutations of 10 questions, subtract the number of (b) to get the answer\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     10! - 2*9! = 725760 = 3628800 - 725760 = 2903040.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "Solved.  All questions are answered.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This problem is about PERMUTATIONS.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "On Permutations, &nbsp;see introductory lessons \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Permutations.lesson>Introduction to Permutations</A>\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-permutations.lesson>PROOF of the formula on the number of Permutations</A>\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Problems-on-Permutations.lesson>Problems on Permutations</A>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Permutations/OVERVIEW-the-lessons-on-Permutations-and-Combinations.lesson>OVERVIEW of lessons on Permutations and Combinations</A>\r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The referred lessons are the part of this online textbook under the topic &nbsp;\"<U>Combinatorics: Combinations and permutations</U>\". \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Save the link to this textbook together with its description\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "into your archive and use when it is needed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );