document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199754>Question 199754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> May someone can help me with:\r<BR>\n" );
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document.write( "In how many ways can 2 men, 4 women, 3 boys, 3 girls be selected from 6 men, 8 women, 4 boys and 5 girls if a particular man and a particular woman must be selected?\r<BR>\n" );
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document.write( "The answer is 7000 but I get 14000:\r<BR>\n" );
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document.write( "{5!/(2!3!)} x {7!/(4!3!)} x {4!/3!} x {5!/(2!3!)} \r<BR>\n" );
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document.write( "for the men, I take 5! because there are (6-1) men remaining: one has been selected already;\r<BR>\n" );
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document.write( "for the women, I take 7! because there are (8-1) women remaining: one has been selected already;\r<BR>\n" );
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document.write( "Thanks a lot! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150129 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=150129\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "You have one very small error.  Actually, you made the same error twice, but one of the instances did not affect the outcome of the calculation.\r<BR>\n" );
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document.write( "You were absolutely correct to assume that, because one of the men was already chosen, that you were selecting from a group of 5 rather than 6.  Likewise, since a woman was pre-selected, you are selecting from 7 rather than 8.\r<BR>\n" );
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document.write( "The problem is, in the case of your calculation for the number of combinations for the men, not only are you selecting from a group that has been reduced by 1, the number you need to select is also reduced by 1.\r<BR>\n" );
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document.write( "Hence, the combination calculation for the men must be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ _5C_1 = \frac{5!}{1!(5-1)!} = 5\">\r<BR>\n" );
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document.write( "It appears that you made the same error when you did the combinations calculation for the women, but here there is no impact on the calculation because:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ _7C_3 = \frac{7!}{3!(7-3)!} = \frac{7!}{4!(7-4)!} =\ _7C_4\">\r<BR>\n" );
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document.write( "So you can see that the error didn't make any difference at that point.\r<BR>\n" );
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document.write( "Bottom line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5 \times 35 \times 4 \times 10 = 7000\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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