document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197379>Question 1197379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Six students are to line up for a photograph.\r<BR>\n" );
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document.write( "a) In how many ways can the 6 students standing in a line be arranged?\r<BR>\n" );
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document.write( "b) In how many ways can the 6 students standing in a line be arranged if Jill must be first?\r<BR>\n" );
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document.write( "c) In how many ways can 6 students standing in a line be arranged if Jill must be first and Meera last? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830611 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</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=830611\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "(a)  in 6! = 6*5*4*3*2*1 = 720 different line arrangements.\r\n" );
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document.write( "     The number of permutations of n objects is n! = 1*2*3* . . . *n.\r\n" );
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document.write( "     The number of permutations of 6 objects is 6! = 1*2*3* . . . *6 = 720.\r\n" );
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document.write( "     Or use this mantra\r\n" );
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document.write( "       - any of 6 students can stay in 1st position (giving 6 options)\r\n" );
document.write( "       - any of 5 remaining students can stay  in 2nd position (giving 5 options)\r\n" );
document.write( "       - any of 4 remaining students can stay  in 3rd position (giving 4 options)\r\n" );
document.write( "                . . . and so on . . . \r\n" );
document.write( "       - any of 2 remaining students can stay  in 5th position (giving 2 options)\r\n" );
document.write( "       -          remaining last student stays in 6th position (giving only 1 options).\r\n" );
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document.write( "      Then you multiply the number of options and get 6!.\r\n" );
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document.write( "(b)  5! = 120, because the first position is just occupied,\r\n" );
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document.write( "         and only 5 remaining students can permutate in 5 remaining positions.\r\n" );
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document.write( "        \r\n" );
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document.write( "(c)  4! =  24, because the 1st position and the 6th position are just occupied,\r\n" );
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document.write( "         and only 4 remaining students can permutate in 4 remaining positions.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved, answered and thoroughly explained.\r<BR>\n" );
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document.write( "---------------\r<BR>\n" );
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document.write( "This problem teaches you on PERMUTATIONS.\r<BR>\n" );
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document.write( "On &nbsp;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( "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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document.write( " </SPAN>\n" );
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