document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=459764>Question 459764</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many arrangements are there of all the letters in PUPPIES if : The 3Ps must be together? The arrangement must begin and end with a P?\r<BR>\n" );
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document.write( "My work:\r<BR>\n" );
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document.write( "7P3 x 7P4  ?\r<BR>\n" );
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document.write( "3P1 x 6P5 x 3P1 ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #315318 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=315318\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You should note that the P's are indistinguishable if you are looking for distinct arrangements.\r<BR>\n" );
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document.write( "If the 3 P's must be together, we can treat the three P's as one giant letter. Then, there are four \"letters\" to be arranged, creating 4P4 = 24 arrangements.\r<BR>\n" );
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document.write( "If the arrangement must begin and end with a P, then we have the letters E, I, P, S, and U to arrange in the center. Here, there are 5P5 = 120 arrangements.\r<BR>\n" );
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document.write( "Note that I did not treat the P's as being distinct. </SPAN>\n" );
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