document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157483>Question 1157483</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question:a committee of 3 boys and 4 girls is to be formed from 5 boys and 6 girls. How many committees are possible if one girl refuses to serve if a certain other girl is chosen<BR>\n" );
document.write( "My calculation :5c3 x 5c4 =50,but the answer given is 90 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #780353 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52876)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=780353\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "You should calculate the TOTAL possible number of combinations,\r<BR>\n" );
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document.write( "and then SUBTRACT from it the number of PROHIBITED combinations.\r<BR>\n" );
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document.write( "Does it work for you ?\r<BR>\n" );
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document.write( "Does it give you the right idea on how to move ahead ?\r<BR>\n" );
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document.write( "You may report me about your progress.\r<BR>\n" );
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document.write( "On Combinations, &nbsp;see introductory lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Permutations/OVERVIEW-the-lessons-on-Permutations-and-Combinations.lesson>OVERVIEW of lessons on Permutations and Combinations</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic &nbsp;\"<U>Combinatorics: Combinations and permutations</U>\". \r<BR>\n" );
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document.write( "Save the link to this textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "into your archive and use when it is needed.\r<BR>\n" );
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document.write( "Comment from student: Thanks for your reply but I can't get the idea to calculate the prohibited combination <BR>\n" );
document.write( "My new calculation : (5c3 X 6c4)-(5c4x5c3)=100 Still didn't get the correct answer...<BR>\n" );
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document.write( "<U>My response</U> :\r<BR>\n" );
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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( "    The number of all combinations of 4G from 6G  is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B6%5D%5E4 ALIGN=MIDDLE  ALT=\"C%5B6%5D%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "    Of them, the prohibited combinations are those that contain these two anti-pathic girls.\r\n" );
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document.write( "    The number of these prohibited combinations for girls is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B4%5D%5E2 ALIGN=MIDDLE  ALT=\"C%5B4%5D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:  \r\n" );
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document.write( "         you construct these prohibited combinations taking 2 antipathic girls, \r\n" );
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document.write( "         and then you add to them 2 girls from remaining 6-2 = 4 \"regular\" girls.\r\n" );
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document.write( "    So, for girls the number of prohibited teams is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B4%5D%5E2 ALIGN=MIDDLE  ALT=\"C%5B4%5D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2A3%29%2F%281%2A2%29 ALIGN=MIDDLE  ALT=\"%284%2A3%29%2F%281%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F2 ALIGN=MIDDLE  ALT=\"12%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6.\r\n" );
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document.write( "    You should combine them with all possible teams of boy, and it is what you should subtract from yours very first and most bigger number.\r\n" );
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document.write( "That's all.\r<BR>\n" );
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document.write( "Please let me know, if you do understand my explanations, and also whether you were able to complete the solution in full.\r<BR>\n" );
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document.write( "Happy solving (!)\r<BR>\n" );
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document.write( "<U>Comment from student</U> :  I have fully understand your explanation Thank you!!!!!\r<BR>\n" );
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document.write( " (5c3 x 6c4)-(5c3 x 4c2) = 90<BR>\n" );
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document.write( "<U>My response</U> :  You are absolutely right.\r<BR>\n" );
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document.write( "Your answer is correct !\r<BR>\n" );
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document.write( "My congratulations !\r<BR>\n" );
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document.write( "I am very glad to see your progress.\r<BR>\n" );
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document.write( "It is our common achievement: my in explanation, your in understanding.\r<BR>\n" );
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document.write( "To celebrate this breakthrough, I have a gift for you.\r<BR>\n" );
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document.write( "It is the list of additional (introductory) problems in elementary theory of probability in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Simple-and-simplest-probability-problems.lesson>Simple and simplest probability problems</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Solving-probability-problems-using-complementary-probability.lesson>Solving probability problems using complementary probability</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-Probability-problems-related-to-Combinations.lesson>Elementary Probability problems related to combinations</A> (*)\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/A-True-False-test.lesson>A True/False test</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/A-multiple-choice-answers-test.lesson>A multiple choice answers test</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Conditional-probability-problems.lesson>Conditional probability problems</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Typical-probability-problems-from-the-archive.lesson>Typical probability problems from the archive</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Experimental-probability-problems.lesson>Experimental probability problems</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-operations-on-sets-help-solving-Probability-problems.lesson>Elementary operations on sets help solving Probability problems</A> \r<BR>\n" );
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document.write( "Although these problems are on Probability theory, they have many in common with Combinatorics problems.\r<BR>\n" );
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document.write( "In particular, the lesson, marked (*) in the list, contains many problems, that are close to the solved current problem.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic &nbsp;\"<U>Solved problems on Probability</U>\". \r<BR>\n" );
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document.write( "Save the link to this textbook together with its description\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "into your archive and use when it is needed.\r<BR>\n" );
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document.write( "Consider these lessons as your textbook,  &nbsp;handbook,  &nbsp;a Solutions Manual, &nbsp;tutorials and &nbsp;(free of charge)  &nbsp;home teacher.\r<BR>\n" );
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document.write( "Happy learning (!)\r<BR>\n" );
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document.write( "Come again to this forum soon to learn something new (!)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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