document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=293160>Question 293160</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Four children Alice, Brad, Cathy and Dan are arranged in a line. If Brad and Cathy cannot be next to each other, in how many ways can the kids be arranged?\r<BR>\n" );
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document.write( "A) 6     (B) 12     (C) 14     (D) 16     (E) 24  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #211613 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=211613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It would be 24 if there were no restrictions<BR>\n" );
document.write( "For each in first position there are 6 ways 4*3*2*1<BR>\n" );
document.write( "(abcd)  bacd    cabd   (dabc)<BR>\n" );
document.write( "abdc    badc    cadb   (dacb)<BR>\n" );
document.write( "(acbd) (bcad)  (cbda)  dbac<BR>\n" );
document.write( "acdb   (bcda)  (cbad)  (dbca)<BR>\n" );
document.write( "(adbc)  bdac    cdab   dcab<BR>\n" );
document.write( "(adcb)  bdca    cdba   (dcba)<BR>\n" );
document.write( "With the restriction we have 2+4+4+2=12<BR>\n" );
document.write( "Brad and Cathy can't be next to each other.<BR>\n" );
document.write( "All combos of bc and cb are eliminated<BR>\n" );
document.write( "Either in 1st and 2nd position<BR>\n" );
document.write( "bcad bcda<BR>\n" );
document.write( "cbad cbda<BR>\n" );
document.write( "either in 2nd and 3rd<BR>\n" );
document.write( "abcd dbca<BR>\n" );
document.write( "acbd dcba<BR>\n" );
document.write( "either in 3rd and 4th<BR>\n" );
document.write( "adbc dabc<BR>\n" );
document.write( "adcb dacb<BR>\n" );
document.write( "That removes 12 leaving 12<BR>\n" );
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