document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169264>Question 1169264</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On my bookshelf I have 5 books of poetry, 15 graphic novels, 8 biographies and 3 self-help books.  I plan to take 7 books with me on my vacation.\r<BR>\n" );
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document.write( "a)In how many different ways can I take 7 books with me on my vacation?<BR>\n" );
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document.write( "b)In how many different ways can my 7 books consist of 2 books of poetry, 3 graphic novels and 2 self-help books?\r<BR>\n" );
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document.write( "c)In how many different ways can my 7 books consist of exactly 3 graphic novels?\r<BR>\n" );
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document.write( "d)In how many different ways can my 7 books consist of at least 6 biographies? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793920 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</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=793920\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "On my bookshelf I have 5 books of poetry, 15 graphic novels, 8 biographies and 3 self-help books. <BR>\n" );
document.write( "I plan to take 7 books with me on my vacation.<BR>\n" );
document.write( "a)In how many different ways can I take 7 books with me on my vacation?\r<BR>\n" );
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document.write( "b)In how many different ways can my 7 books consist of 2 books of poetry, 3 graphic novels and 2 self-help books?<BR>\n" );
document.write( "c)In how many different ways can my 7 books consist of exactly 3 graphic novels?<BR>\n" );
document.write( "d)In how many different ways can my 7 books consist of at least 6 biographies?<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( "(b)  In how many different ways can my 7 books consist of 2 books of poetry, 3 graphic novels and 2 self-help books?\r\n" );
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document.write( "     You can select 2 books of poetry from  5 books of poetry by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B5%5D%5E2 ALIGN=MIDDLE  ALT=\"C%5B5%5D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2A4%29%2F%281%2A2%29 ALIGN=MIDDLE  ALT=\"%285%2A4%29%2F%281%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10 ways.\r\n" );
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document.write( "     You can select 3 graphic novels  from 15 graphic novels  by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B15%5D%5E3 ALIGN=MIDDLE  ALT=\"C%5B15%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2A14%2A13%29%2F%281%2A2%2A3%29 ALIGN=MIDDLE  ALT=\"%2815%2A14%2A13%29%2F%281%2A2%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 455 ways.\r\n" );
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document.write( "     You can select 2 self-help books  from 3 self-help books  by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B3%5D%5E2 ALIGN=MIDDLE  ALT=\"C%5B3%5D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A2%29%2F%281%2A2%29 ALIGN=MIDDLE  ALT=\"%283%2A2%29%2F%281%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3 ways.\r\n" );
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document.write( "     Since these selections are INDEPENDENT in separate categories, the total number of choices is the product 10*455*3 = 13650,\r\n" );
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document.write( "        according to the <U>foundamental counting principle</U>.\r\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/Fundamental-counting-principle-problems.lesson>Fundamental counting principle 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/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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