document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106668>Question 1106668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many ways can you choose 3 flowers from an arrangement of 5? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721661 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=721661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "The number of ways to choose 3 things from the set of 5 things is  \r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B5%5D%5E3 ALIGN=MIDDLE  ALT=\"C%5B5%5D%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%21%2F%283%21%2A%285-3%29%21%29 ALIGN=MIDDLE  ALT=\"5%21%2F%283%21%2A%285-3%29%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%21%2F%283%21%2A2%21%29 ALIGN=MIDDLE  ALT=\"5%21%2F%283%21%2A2%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2A2%2A3%2A4%2A5%29%2F%28%281%2A2%2A3%29%2A%281%2A2%29%29 ALIGN=MIDDLE  ALT=\"%281%2A2%2A3%2A4%2A5%29%2F%28%281%2A2%2A3%29%2A%281%2A2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = cancel 3! = 1*2*3 in both the numerator and denominator = <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;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F2 ALIGN=MIDDLE  ALT=\"20%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10.\r\n" );
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document.write( "In general case, the number of ways to choose \"m\" things from the set of \"n\" things (n > m) is \r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bn%5D%5Em ALIGN=MIDDLE  ALT=\"C%5Bn%5D%5Em\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28m%21%2A%28n-m%29%21%29 ALIGN=MIDDLE  ALT=\"n%21%2F%28m%21%2A%28n-m%29%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28m%21%2A%28n-m%29%21%29 ALIGN=MIDDLE  ALT=\"n%21%2F%28m%21%2A%28n-m%29%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2A%28n-1%29%2A%28n-2%29%2A+ellipsis%2A%28n-m%2B1%29%29%2F%281%2A2%2Aellipsis%2Am%29 ALIGN=MIDDLE  ALT=\"%28n%2A%28n-1%29%2A%28n-2%29%2A+ellipsis%2A%28n-m%2B1%29%29%2F%281%2A2%2Aellipsis%2Am%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "It is called the \"number of combinations of n items taken m at a time\".\r\n" );
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document.write( "On combinations, 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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