document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=48480>Question 48480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Signals are sent from a battleship by placing four flags on a vertical pole.  How many different signals can be formed by selecting the four flags from\r<BR>\n" );
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document.write( "1.  Four different colored flags\r<BR>\n" );
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document.write( "2.  Two different red flags & two identical white flags </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #32079 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=32079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1 4 different red flags:\r<BR>\n" );
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document.write( "first flag: 4 possibles<BR>\n" );
document.write( "second flag: 3 possibles (since one has been chosen as the first flag)<BR>\n" );
document.write( "third flag: 2 possibilities<BR>\n" );
document.write( "fourth flag: 1 possible flag.\r<BR>\n" );
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document.write( "Total: 4*3*2*1 --> 24 possible ways\r<BR>\n" );
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document.write( "2. 2 different red flags (r and R) and 2 identical white flags (W and W)\r<BR>\n" );
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document.write( "Permutations are, in order:<BR>\n" );
document.write( "rRWW<BR>\n" );
document.write( "rWRW<BR>\n" );
document.write( "rWWR\r<BR>\n" );
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document.write( "RrWW<BR>\n" );
document.write( "RWrW<BR>\n" );
document.write( "RWWr\r<BR>\n" );
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document.write( "WWrR<BR>\n" );
document.write( "WWRr<BR>\n" );
document.write( "WrRW<BR>\n" );
document.write( "WRrW<BR>\n" );
document.write( "WrWR<BR>\n" );
document.write( "WRWr\r<BR>\n" );
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document.write( "so answer is 12. Now algebraically we get this by starting with the 24 as the answer for 4 different flags and then dividing by 2! since we have 2 identical flags (the white ones):\r<BR>\n" );
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document.write( "24/2!<BR>\n" );
document.write( "24/2<BR>\n" );
document.write( "12\r<BR>\n" );
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document.write( "Hope this is clear.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
document.write( " </SPAN>\n" );
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