document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1052575>Question 1052575</A>: <I><SPAN STYLE=\"word-break: break-all;\">  hey i'm having trouble on this question i've tried 7 times and different equations but i just cant get it:<BR>\n" );
document.write( " There are 24 students in your class. Your teacher wants to put you in groups for your data-<BR>\n" );
document.write( "management project. How many ways can six groups of four be made if\r<BR>\n" );
document.write( "\n" );
document.write( "A)there are no restrictions\r<BR>\n" );
document.write( "\n" );
document.write( "Answer=4.509 x 10^12 (will also accept 3.247 x 10^15)\r<BR>\n" );
document.write( "\n" );
document.write( "Thankyou.:)\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #667954 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=667954\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i think i found a formulas you are looking for.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i tried:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c(24,4) * c(20,4) * c(16,4) * c(12,4) * c(8,4) * c(4,4)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the answer i got was 3.246670537 * 10^15.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "round that to 3 decimal digits and you get 3.247 * 10^15.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the rationale behind it is as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "out of 24 people, you can make 24c4 groups of 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "once you select 4 of those, there are 20c4 groups of 4 that can be made out of the rest of them.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "once you select 4 of those, there are 16c4 groups of 4 that can be made out of the rest of them.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and so on.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the combination formula used is c(n,x) which can also be shown as ncx.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this formula is n! / (x! * (n-x)!)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for example:  c(24,4) = 24c4 = 24! / (4! * 20!)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i then divided the answer by 6! and i got 4.509 * 10^12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i confess i didn't really know if these formulas would be right, but made some semi-educated guesses that turned out to be right.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so your answer is either:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c(24,4) * c(20,4) * c(16,4) * c(12,4) * c(8,4) * c(4,4)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "or:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c(24,4) * c(20,4) * c(16,4) * c(12,4) * c(8,4) * c(4,4) / 6!.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the division by 6! has to do with taking away ordering of the sets of 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "what you wind up with is multiples sets of 6 groups of 4 with the same elements in each group only in a different arrangement.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the division by 6! takes away the different arrangements.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it's har to explain and even harder to show, but my suspicions were correct and i did come up with the right answer based on what answers were acceptable.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i'm happy just to be able to do that.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "what makes these problems hard is not being able to verify that your formula is correct without going through hoops because the number of possibilities is so large.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i usually try to reduce the number of possibilities and go through the manual labor of identifying each possibility.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that was hard to do in this case, but i was able to do enough to develop my hunches.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "hope this satisfies you.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sorry i can't explain why i did what i did any better.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );