document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=735802>Question 735802</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here is the problem: A soccer team has 16 players. How many ways can the coach choose a starting team of 11 players?\r<BR>\n" );
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document.write( "I have been working on this problem for forever and still am having trouble solving it. Here's what I came up with but I know I'm doing something wrong.\r<BR>\n" );
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document.write( "16!/11!(16-11)! then i write it all out: <BR>\n" );
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document.write( "11! (16-11)!\r<BR>\n" );
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document.write( "16x15x14x13x12x11x10x9x8x7x6x5x4x3x2x1<BR>\n" );
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document.write( "11x10x9x8x7x6x5x4x3x2x1x(5x4x3x2x1)<BR>\n" );
document.write( "it gives me some bizarre number. If you could show how to do the work correctly to get an answer that actually makes sense and explain where I went wrong that would be great. Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #449550 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=449550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a combination problem, that is, how many combinations of 16 players taken 11 at a time are there?  So we have\r<BR>\n" );
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document.write( "the following formula to evaluate\r<BR>\n" );
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document.write( "16! / 11! * (16 - 11)!      we use the combination formula because order does not matter in this problem\r<BR>\n" );
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document.write( "reducing the above formula we get\r<BR>\n" );
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document.write( "(16*15*14*13*12) / 5*4*3*2*1\r<BR>\n" );
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document.write( "further reduction gives us\r<BR>\n" );
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document.write( "8*15*14*13 / 5 = 4368 combinations </SPAN>\n" );
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