document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179275>Question 1179275</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Calculate the total number of different permutations of all letters A, B, C, D, E, F when<BR>\n" );
document.write( "a) there are no restrictions,<BR>\n" );
document.write( "b) the letters A and B are to be adjacent to one another,<BR>\n" );
document.write( "c) the first letter is A, B or C and the last letter is D, E or F.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #808826 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52873)</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=808826\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Calculate the total number of different permutations of all letters A, B, C, D, E, F when<BR>\n" );
document.write( "a) there are no restrictions,<BR>\n" );
document.write( "b) the letters A and B are to be adjacent to one another,<BR>\n" );
document.write( "c) the first letter is A, B or C and the last letter is D, E or F.<BR>\n" );
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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( "(a)  6! = 6*5*4*3*2*1 = 720.\r\n" );
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document.write( "(b)  You concider the pair of letters AB as one glued object;\r\n" );
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document.write( "     so you have  5 object to permutate, in all, which produces 5! = 5*4*3*2*1 = 120 different permutations.\r\n" );
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document.write( "     Another 120 different permutations you have with the object BA instead of AB.\r\n" );
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document.write( "     So, in total, there are  120 + 120 = 240 such permutations.\r\n" );
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document.write( "(c)  You have 3 possibility for the first letter (A, B or C).\r\n" );
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document.write( "     Similarly, you have 3 possibility for the last letter (D, E or F).\r\n" );
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document.write( "     Finally, you have 4! = 4*3*2*1 = 24 permutations for the remaining 6-2 = 4 letters.\r\n" );
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document.write( "     Hence, in all, there are  3*3*24 = 216  possible permutations, satisfying the imposed conditions.\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "On Permutations, &nbsp;see introductory lessons \r<BR>\n" );
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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" );
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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" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Problems-on-Permutations.lesson>Simple and simplest problems on permutations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Permutations/Special-type-permutations-problems.lesson>Special type permutations problems</A> \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( "&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" );
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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 lessons are 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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