document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=789225>Question 789225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the word \"veracious\" <BR>\n" );
document.write( "In how many ways can you arrange the 9 letters such that V and C are never adjacent to each other? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #478776 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=478776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 9! = 9*8*7*6*5*4*3*2*1 = 362,880 different ways to arrange all 9 letters.\r<BR>\n" );
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document.write( "If we think of V and C as one letter, call it z, then we have the \"word\" \"zeraious\" and there are 8! = 8*7*6*5*4*3*2*1 = 40,320 ways to arrange these letters. Double this amount to account for CV to get 2*40,320 = 80,640\r<BR>\n" );
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document.write( "So there are 80,640 words where V and C are together (either as VC or CV)\r<BR>\n" );
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document.write( "So there are 362,880 - 80,640 = <font color=\"red\">282,240</font> different words where V and C are never adjacent to each other. </SPAN>\n" );
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