document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=885176>Question 885176</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The crew of an 8 member rowing team is to be chosen from 12 men , of which 3 can<BR>\n" );
document.write( "on one side only and 2 can on other side only.find number of ways of arranging the <BR>\n" );
document.write( "crew with 4 memembers on each side.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535156 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20055)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=535156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <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( "Let's divide the 12 up into 3 Ls, 2 R's and 7 E's\r\n" );
document.write( "The 3 L's can only row on the Left.\r\n" );
document.write( "The 2 R's can only row on the Right.\r\n" );
document.write( "The 7 E's can row on Either side.\r\n" );
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document.write( "There are 11 cases to consider\r\n" );
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document.write( "Case 1. 1R, 7E's  \r\n" );
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document.write( "Choose the 1R C(2,1) ways\r\n" );
document.write( "Seat the 1R P(4,1) ways\r\n" );
document.write( "Choose and seat the 7E's P(12,7) ways.\r\n" );
document.write( "Total for case 1: \r\n" );
document.write( "C(2,1)P(4,1)P(12,7) = \r\n" );
document.write( "2×4×P(12,7) = 8P(12,7)\r\n" );
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document.write( "Case 2. 2R's, 6E's\r\n" );
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document.write( "Choose the 2R's C(2,2)=1 way, \r\n" );
document.write( "Seat the 2R's P(4,2) ways.\r\n" );
document.write( "Choose and seat the 6E's P(12,6) ways.\r\n" );
document.write( "Total for case 2: \r\n" );
document.write( "C(2,2)P(4,2)P(12,6) =\r\n" );
document.write( "1×12×P(12,6) = 12P(12,6)\r\n" );
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document.write( "Case 3. 1L, 7E's\r\n" );
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document.write( "Choose the 1L C(3,1) ways, \r\n" );
document.write( "Seat the 1L P(4,1) ways\r\n" );
document.write( "Choose and seat the 7E's P(12,7) ways.\r\n" );
document.write( "Total for case 3: \r\n" );
document.write( "C(3,1)C(4,1)P(12,7) =\r\n" );
document.write( "3×4×P(12,7) = 12P(12,7)\r\n" );
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document.write( "Case 4: 1L, 1R, 6E's\r\n" );
document.write( "Choose the 1L C(3,1) ways, \r\n" );
document.write( "Seat the 1L P(4,1) ways,\r\n" );
document.write( "Choose the 1R C(2,1) ways, \r\n" );
document.write( "Seat the 1R C(4,1) ways,\r\n" );
document.write( "Choose and seat the 6E's P(12,6) ways.\r\n" );
document.write( "Total for case 4: \r\n" );
document.write( "C(3,1)C(4,1)C(2,1)C(4,1)P(12,6)=\r\n" );
document.write( "3×4×2×4×P(12,6) = 96P(12,6)\r\n" );
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document.write( "Case 5: 1L, 2R's, 5E's\r\n" );
document.write( "Choose the 1L C(3,1) ways, \r\n" );
document.write( "Seat the 1L P(4,1) ways,\r\n" );
document.write( "Choose the 2R's C(2,2)=1 way, \r\n" );
document.write( "Seat the 2R's P(4,2) ways,\r\n" );
document.write( "Choose and seat the 5E's P(12,5) ways.\r\n" );
document.write( "Total for case 5: \r\n" );
document.write( "C(3,1)P(4,1)C(2,2)P(4,2)P(12,5) =\r\n" );
document.write( "3×4×1×12×P(12,5) = 144P(12,5)\r\n" );
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document.write( "Case 6: 2L's, 6E's\r\n" );
document.write( "Choose the 2L's C(3,2) ways, \r\n" );
document.write( "Seat the 2L's P(4,2) ways,\r\n" );
document.write( "Choose and seat the 6E's P(12,6) ways.\r\n" );
document.write( "Total for case 6: \r\n" );
document.write( "C(3,2)P(4,2)P(12,6)=\r\n" );
document.write( "3×12×P(12,6) = 36P(12,6)\r\n" );
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document.write( "Case 7: 2L's, 1R, 5E's\r\n" );
document.write( "Choose the 2L's C(3,2) ways, \r\n" );
document.write( "Seat the 2L's P(4,2) ways,\r\n" );
document.write( "Choose the 1R C(2,1) ways, \r\n" );
document.write( "Seat the 1R P(4,1) ways\r\n" );
document.write( "Choose and seat the 5E's P(12,5) ways.\r\n" );
document.write( "Total for case 7:\r\n" );
document.write( "C(3,2)P(4,2)C(2,1)P(4,1)P(12,5) =\r\n" );
document.write( "3×12×2×4×P(12,5) = 288P(12,5)\r\n" );
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document.write( "Case 8: 2L's, 2R's, 4E's\r\n" );
document.write( "Choose the 2L's C(3,2) ways, \r\n" );
document.write( "Seat the 2L's P(4,2) ways,\r\n" );
document.write( "Choose the 2R's C(2,2)=1 way, \r\n" );
document.write( "Seat the 2R's P(4,2) ways\r\n" );
document.write( "Choose and seat the 4E's P(12,4) ways.\r\n" );
document.write( "Total for case 8:\r\n" );
document.write( "C(3,2)P(4,2)C(2,2)P(4,2)P(12,4)\r\n" );
document.write( "3×12×1×12×P(12,4) = 432P(12,4).\r\n" );
document.write( "  \r\n" );
document.write( "Case 9: 3L's, 5E's\r\n" );
document.write( "Choose the 3L's C(3,3)=1 way, \r\n" );
document.write( "Seat the 3L's P(4,3) ways,\r\n" );
document.write( "Choose and seat the 5E's P(12,5) ways.\r\n" );
document.write( "Total for case 6: \r\n" );
document.write( "C(3,3)P(4,3)P(12,5)\r\n" );
document.write( "1×24×P(12,5) = 24P(12,5)\r\n" );
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document.write( "Case 10: 3L's, 1R, 4E's\r\n" );
document.write( "Choose the 3L's C(3,3)=1 way, \r\n" );
document.write( "Seat the 3L's P(4,3) ways,\r\n" );
document.write( "Choose the 1R C(2,1) ways,\r\n" );
document.write( "Seat the 1R P(4,1) ways,\r\n" );
document.write( "Choose and seat the 4E's P(12,4) ways.\r\n" );
document.write( "Total for case 10: \r\n" );
document.write( "C(3,3)P(4,3)C(2,1)P(4,1)P(12,4)\r\n" );
document.write( "1×24×2×4×P12,4) = 192P(12,4)\r\n" );
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document.write( "Case 11: 3L's, 2R's, 3E's\r\n" );
document.write( "Choose the 3L's C(3,3)=1 way, \r\n" );
document.write( "Seat the 3L's P(4,3) ways,\r\n" );
document.write( "Choose the R's C(2,2)=1 way,\r\n" );
document.write( "Seat the 2R's P(4,2) ways,\r\n" );
document.write( "Choose and seat the 3E's P(12,3) ways.\r\n" );
document.write( "Total for case 10: \r\n" );
document.write( "C(3,3)P(4,3)C(2,2)P(4,2)P(12,3)\r\n" );
document.write( "1×24×1×12×P(12,3) = 288P(12,3)\r\n" );
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document.write( "Total =\r\n" );
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document.write( "8P(12,7)+12P(12,6)+12P(12,7)+96P(12,6)+\r\n" );
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document.write( "144P(12,5)+36P(12,6)+288P(12,5)+432P(12,4)+\r\n" );
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document.write( "24P(12,5)+192P(12,4)+288P(12,3) = \r\n" );
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document.write( "(8+12)P(12,7)+(12+96+36)P(12,6)+\r\n" );
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document.write( "(144+288+24)P(12,5)+(432+192)P(12,4)+\r\n" );
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document.write( "288P(12,3) =\r\n" );
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document.write( "20P(12,7)+144P(12,6)+456P(12,5)+624P(12,4)+288P(12,3) =\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2A%2812%21%29%2F%28%2812-7%29%21%29%2B144%2A%2812%21%29%2F%28%2812-6%29%21%29%2B456%2A%2812%21%29%2F%28%2812-5%29%21%29%2B624%2A%2812%21%29%2F%28%2812-4%29%21%29%2B288%2A%2812%21%29%2F%28%2812-3%29%21%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
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document.write( "Answer =  226765440\r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
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