document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201865>Question 1201865</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following 7 × 22 grid is divided into squares that are 1 unit by 1 unit.<BR>\n" );
document.write( "WebAssign PlotThe shortest possible path on this grid from A to B is 29 units long. One such path is shown in the figure. Let X be the set of all 29-unit-long paths from A to B.\r<BR>\n" );
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document.write( "Compute |X|, the number of 29-unit-long paths from A to B.<BR>\n" );
document.write( "|X| =  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836407 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=836407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The figure is described as a 7x22 grid of unit squares, so we don't need to see the figure....<br><BR>\n" );
document.write( "Assuming this is a problem where A and B are opposite corners of the grid, the number of paths of length 29 from A to B is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29%21%2F%28%2822%21%29%287%21%29%29 ALIGN=MIDDLE  ALT=\"29%21%2F%28%2822%21%29%287%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To understand the reason for that answer, let B be 22 units to the right of A and 7 units above A.  Then any path from A to B of length 29 has to move 22 \"steps\" to the right (\"R\") and 7 steps up (\"U\").<br><BR>\n" );
document.write( "So each path of length 29 from A to B consists of some arrangement of the symbols<br><BR>\n" );
document.write( "RRRRRRRRRRRRRRRRRRRRRRUUUUUUU<br><BR>\n" );
document.write( "By a well-known counting principle, the number of ways to do that is the number shown above.<br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29%21%2F%28%2822%21%29%287%21%29%29 ALIGN=MIDDLE  ALT=\"29%21%2F%28%2822%21%29%287%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
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