document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=611286>Question 611286</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm really confused about permutations, and especially this problem!<BR>\n" );
document.write( "\"Flags of 6 countries are to be displayed in a row. The flags of two countries, A and B, must be next to each other.<BR>\n" );
document.write( "a) In how many ways can this be done if the flag of country A must be to the left of the flag of country B?<BR>\n" );
document.write( "(The answer key says 120, but I don't understand how)<BR>\n" );
document.write( "b) In how many orders can the flags be displayed if the 2 flags can be in either order?<BR>\n" );
document.write( "(The answer key says 240 but I don't understand how)\"<BR>\n" );
document.write( "Thank you so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #384887 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=384887\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: I'm assuming that all 6 flags are different and that order matters.\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "Since A and B must be next to each other AND A must be to the left of B, this means that we can effectively \"combine\" the two flags to make a third flag (say AB). This is not a single flag, but because the two can't be separated or ordered differently, we can group the two like this.\r<BR>\n" );
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document.write( "So we have the 5 flags:  AB, C, D, E, F\r<BR>\n" );
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document.write( "Where AB is considered one flag.\r<BR>\n" );
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document.write( "From here, there are 5! = 5*4*3*2*1 = 120 different ways to order these five flags.\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "This is a lot like part A, but now we consider the case that we're dealing with the \"flag\" BA\". This will double the number in part a) to give you 2*120 = 240 \r<BR>\n" );
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document.write( "Let me know if this makes sense. Thanks.<BR>\n" );
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