document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=514874>Question 514874</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In how many ways can 6 men and 4 women sit in a row if the men must sit together and the women must sit together.\r<BR>\n" );
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document.write( "I thought it was 6!4! = 17280 possible arrangements but now I am second guessing.\r<BR>\n" );
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document.write( "Thanks for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #343602 by </B><A HREF=/tutors/aboutme.mpl?userid=drcole><B>drcole(72)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drcole><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=343602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are correct that there are 6! = 720 ways that we could arrange six men in a row, and 4! = 24 ways to arrange four women in a row, but since all of the men and all of the women need to sit together, we also have to take into account how the two groups are arranged:\r<BR>\n" );
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document.write( "MMMMMMFFFF  or  FFFFMMMMMM\r<BR>\n" );
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document.write( "So there are actually 6!4!2 = (720)(24)(2) = 34,560 ways to rearrange the six men and four women as specified. </SPAN>\n" );
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