document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116313>Question 1116313</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 4 freshman, 6 sophomores, 7 juniors, and 3 seniors on a school field trip. If three students are randomly selected to carry water bottle cases, what is the probability that they are all juniors?\r<BR>\n" );
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document.write( "Would it be 7/13? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #731200 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=731200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "In all, there are 4 + 6 + 7 + 3 = 20 students.\r\n" );
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document.write( "By selecting randomly 3 students of 20, you can do it in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B20%5D%5E3 ALIGN=MIDDLE  ALT=\"C%5B20%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2A19%2A18%29%2F%281%2A2%2A3%29 ALIGN=MIDDLE  ALT=\"%2820%2A19%2A18%29%2F%281%2A2%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1140 ways.\r\n" );
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document.write( "In how many ways can you select the group of 3 juniors ?\r\n" );
document.write( "You select them from the sub-group of 7 junior students, therefore, you can do it in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B7%5D%5E3 ALIGN=MIDDLE  ALT=\"C%5B7%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2A6%2A5%29%2F%281%2A2%2A3%29 ALIGN=MIDDLE  ALT=\"%287%2A6%2A5%29%2F%281%2A2%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 35 ways.\r\n" );
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document.write( "Therefore, the probability under the question is  this number  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2F1140 ALIGN=MIDDLE  ALT=\"35%2F1140\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.031 = 3.1%.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "In order to solve freely such problems, you need to know about Combinations.\r<BR>\n" );
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document.write( "On Combinations, &nbsp;see the 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( " </SPAN>\n" );
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