document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159623>Question 1159623</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many arrangements of the word ACTIVE are there if the C and E\r<BR>\n" );
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document.write( "a) must always be together?<BR>\n" );
document.write( "b)must never be together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782757 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52778)</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=782757\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "(a)  If the C and E are always together, we can consider this pair as one merged object.\r\n" );
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document.write( "     Then we have 5 objects in total that admit 5! = 1*2*3*4*5 = 120 permutations.\r\n" );
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document.write( "     But the merged object has two states: CE and EC.\r\n" );
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document.write( "     By combining all these permutations, we have, in total, 2*5! = 2*120 = 240 permutations.\r\n" );
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document.write( "     It is the <U>ANSWER</U> in this case.\r\n" );
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document.write( "(b)  This time, we should consider all permutations of 6 letters of the word ACTIVE, 6! = 720 permutations, \r\n" );
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document.write( "      and subtract those 2*120 = 240 permutations, found in the case (a), where the letters C and E are placed together.\r\n" );
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document.write( "      So, the <U>ANSWER</U>  in this case is  6! - 2*5! = 720 - 240 = 480.\r\n" );
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document.write( "Solved, answered, explained and completed.\r<BR>\n" );
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document.write( "For many other similar solved problems, see the lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Permutations/How-many-different-permutations-may-exist-ubder-given-restrictions.lesson>Problems on Permutations with restrictions</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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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" );
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document.write( "The referred lesson is the part of this online textbook under the topic &nbsp;\"<U>Combinatorics: Combinations and permutations</U>\". \r<BR>\n" );
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document.write( "Save the link to this textbook together with its description\r<BR>\n" );
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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" );
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document.write( "into your archive and use when it is needed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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