document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30470>Question 30470</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many ordered triples (X,Y,Z) of postive intgers satisfy X*Y*Z=4000? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17122 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=17122\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  X*Y*Z=4000 = 4*(2*5)^3 = 2^5* 5^3.\r<BR>\n" );
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document.write( " so X, Y, Z are in the form 2^i * 5^j  (X= 2^i1 * 5^j1,..<BR>\n" );
document.write( " with i1+i2+i3 = 5 and j1+j2+j3 = 3.\r<BR>\n" );
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document.write( " there are C(3+5-1, 5) = C(7,5) = 21 possible i's(why?)<BR>\n" );
document.write( " and C(3+3-1, 3) = C(5,3) = 10 possible j's\r<BR>\n" );
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document.write( " Totally, there are 21*10 = 21 possible ordered triples (X,Y,Z).\r<BR>\n" );
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document.write( " Try X*Y = 2^3* 5^2\r<BR>\n" );
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document.write( " Kenny\r<BR>\n" );
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document.write( " </SPAN>\n" );
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