document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203273>Question 1203273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The letters of the word PROBABILITY are arranged at random. Find the number of arrangements where the two Is are separated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838710 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838710\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The comment from tutor @ikleyn is correct.  In counting the number of arrangements with the two I's together, there is only one way to arrange those two I's, because they are the same letter.<br><BR>\n" );
document.write( "The total number of arrangements is of 11 letters including 2 pairs.  That number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%21%29%2F%28%282%21%29%282%21%29%29 ALIGN=MIDDLE  ALT=\"%2811%21%29%2F%28%282%21%29%282%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For the number of arrangements with the 2 I's together, treat them as a single unit.<br><BR>\n" );
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document.write( "NO!...  Then there are 10 items with one (other) pair; and the two I's in the unit can be arranged in either of 2 orders.  This number is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%28%2810%21%29%2F%282%21%29%29 ALIGN=MIDDLE  ALT=\"%282%29%28%2810%21%29%2F%282%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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document.write( "Yes...  Then there are 10 items with one (other) pair.  the number of arrangements here is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%21%29%2F%282%21%29 ALIGN=MIDDLE  ALT=\"%2810%21%29%2F%282%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Subtract the second number from the first to get the number of arrangements in which the two I's are separated (i.e, not together).<br><BR>\n" );
document.write( "You can do the actual calculations....<br><BR>\n" );
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