document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=473509>Question 473509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear math teacher, \r<BR>\n" );
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document.write( "I am having difficulites solving the following math problem: \r<BR>\n" );
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document.write( "In how many ways can 9 different prizes be awarded to two students so that one receives 3 and the other 6? \r<BR>\n" );
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document.write( "So far, I got two answers but they are incorrect. The correct answer is 168. \r<BR>\n" );
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document.write( "Here is what I did so far: <BR>\n" );
document.write( "First, I said to myself, this might be done this way:  Permutation = 9 factorial divided by (3 factorial times 6 factorial) and that equals to 84. However, that's not the right answer. So then, I calculated: Permutation of 9 things taken 3 at a time TIMES Permution of 6 things taken 6 at time = 82.080. However, it's not the right answer either.  \r<BR>\n" );
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document.write( "Would you please help me solve this problem?  Thank you so much. \r<BR>\n" );
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document.write( "Yours, \r<BR>\n" );
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document.write( "I. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #324726 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=324726\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's say there are 2 students A and B\r<BR>\n" );
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document.write( "Let's focus on how many ways to assign 3 prizes to student A.\r<BR>\n" );
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document.write( "There are 9*8*7 = 504 different ways to assign 3 prizes (out of 9) to student A where order matters. Since order does NOT matter, we divide by 3! = 6 to get 504/6 = 84. Note: this is to ignore combinations that have been counted more than once.\r<BR>\n" );
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document.write( "So there are 84 ways to assign 3 prizes to student A where order does NOT matter.\r<BR>\n" );
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document.write( "Now do the same work for student B to get 84 different ways as well. Basically repeat the above, but replace \"Student A\" with \"Student B\".\r<BR>\n" );
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document.write( "So there are 84+84=168 different ways to assign 3 prizes to one student and 6 prizes to the other. </SPAN>\n" );
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