document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=478404>Question 478404</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear math teacher, \r<BR>\n" );
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document.write( "I am having difficulties with the following problem.  \r<BR>\n" );
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document.write( "How many baseball nines can be chosen from 13 candidates if A, B, C, D are the only candidates for two positions and can play no other position? \r<BR>\n" );
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document.write( "I think I need to select 9 canditates from 13 but I also have 4 candidates (A, B, C, D) for 2 positions. If A, B, C, D can play no othe position but can fill only 2 positions, \r<BR>\n" );
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document.write( "13C9 times 4P2 = 8580 selections but my answer is supposed to be only 216. Where did I make a mistake? \r<BR>\n" );
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document.write( "Thank you for your time. \r<BR>\n" );
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document.write( "Ivanka </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #327843 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=327843\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> knowing what the answer should be makes it a lot easier.<BR>\n" );
document.write( "you have a nice target to shoot for.<BR>\n" );
document.write( "13C9 would be the answer if you had no restrictions.<BR>\n" );
document.write( "given that you have restrictions, you have to modify the equations to fit those restrictions.<BR>\n" );
document.write( "4 people can only play 2 positions.<BR>\n" );
document.write( "the number of ways this can happen are 4C2 = 6<BR>\n" );
document.write( "that leave 9 people for the remaining 7 positions.<BR>\n" );
document.write( "the number of ways that can happen is 9C7 = 36<BR>\n" );
document.write( "the total number of ways both can happen is 36*6 = 216<BR>\n" );
document.write( "bring the numbers down low and you can see what is happening.<BR>\n" );
document.write( "suppose 5 people for 2 positions.<BR>\n" );
document.write( "2 people can only play 1 of the positions.<BR>\n" );
document.write( "that means your equation becomes:<BR>\n" );
document.write( "2C1 * 3C1 = 2*3 = 6<BR>\n" );
document.write( "2C1 is the 2 people for the 1 position.<BR>\n" );
document.write( "3C1 is the remaining 3 people for the other position.<BR>\n" );
document.write( "now assume the people were abcde<BR>\n" );
document.write( "a is person 1<BR>\n" );
document.write( "b is person 2, etc.<BR>\n" );
document.write( "suppose a and b can only play the first position.<BR>\n" );
document.write( "your possible choices for the first position are:<BR>\n" );
document.write( "a<BR>\n" );
document.write( "b<BR>\n" );
document.write( "your possible choices for the other position are:<BR>\n" );
document.write( "c<BR>\n" );
document.write( "d<BR>\n" );
document.write( "e<BR>\n" );
document.write( "you have 2 possible choices for position 1 and 3 possible choices for position 2.<BR>\n" );
document.write( "the total number of possible ways you can outfit this team is 2*3 = 6<BR>\n" );
document.write( "those ways are shown below:<BR>\n" );
document.write( "<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" );
document.write( "        position 1       position 2\r\n" );
document.write( "            a                c\r\n" );
document.write( "            a                d\r\n" );
document.write( "            a                e\r\n" );
document.write( "            b                c\r\n" );
document.write( "            b                d\r\n" );
document.write( "            b                e\r\n" );
document.write( "</PRE><BR>\n" );
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