document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204839>Question 1204839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There is a group of five children, where two of the children are twins. In how<BR>\n" );
document.write( "many ways can I distribute 18 identical pieces of candy to the children, if the<BR>\n" );
document.write( "twins must get 7 pieces of candy? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841369 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=841369\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The statement of the problem is not clear, leading to different possible interpretations.  My interpretation differs from that shown in the response from tutor @Edwin in two ways. (1) The problem does not say that each child must get at least one candy, so the numbers each child gets are non-negative integers, not positive integers. (2) The number of candies each of the twins gets is not important; the only requirement is that together they get 7 pieces.<br><BR>\n" );
document.write( "With that interpretation....<br><BR>\n" );
document.write( "Take the 7 pieces of candy and give them to the twins (to be shared between them in any way).<br><BR>\n" );
document.write( "That leaves 11 pieces of candy to be divided among the other three children.  Using the \"stars and bars\" process, there are 11 stars (the pieces of candy) and 2 bars (to divided the stars (candies) into 3 groups). The number of ways to distribute the candies is then the number of ways of arranging the symbols<br><PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "By a well-known counting principle, that number ways is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%21%2F%28%2811%21%29%282%21%29%29=C%2813%2C2%29=78 ALIGN=MIDDLE  ALT=\"13%21%2F%28%2811%21%29%282%21%29%29=C%2813%2C2%29=78\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER (with this interpretation): 78<br><BR>\n" );
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