document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033270>Question 1033270</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Anthony wants to visit the 20 colleges? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #648004 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=648004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> THE FIFTH GRADER'S THOUGHT:<BR>\n" );
document.write( "Anthony lets luck of the draw decide.<BR>\n" );
document.write( "He writes the name of each college on a small piece of paper, and<BR>\n" );
document.write( "puts the pieces of paper in a bag to draw the names at random.<BR>\n" );
document.write( "He draws the first piece of paper, and marks it as the first college where he will spend a night.<BR>\n" );
document.write( "Of course, he does not put that piece of paper back in the bag, before drawing again to find another college where he will spend a night.<BR>\n" );
document.write( "He then draws {\"without replacement\") a second and a third piece of paper that decide where he will spend the second and third nights respectively.<BR>\n" );
document.write( "That decides the schedule of college sleepovers.<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A9%2A8=720 ALIGN=MIDDLE  ALT=\"10%2A9%2A8=720\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible schedules<BR>\n" );
document.write( "(10 possibilities for the first draw, 9 for the second, and 8 for the third draw).<BR>\n" );
document.write( "However, each set of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > pieces of papers could be drawn in<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A2%2A1=6 ALIGN=MIDDLE  ALT=\"3%2A2%2A1=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > orders, and it would still be the same set, just different orders.<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720 ALIGN=MIDDLE  ALT=\"720\"   DISABLED_style= \"max-width:90%; height:auto;\" > different college sleepover schedules,<BR>\n" );
document.write( "but they represent <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2F6=120 ALIGN=MIDDLE  ALT=\"720%2F6=120\"   DISABLED_style= \"max-width:90%; height:auto;\" > different sets of sleepover college choices.<BR>\n" );
document.write( "The chances that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > particular set of colleges could be chosen that way is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120 ALIGN=MIDDLE  ALT=\"120\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the probability that Anthony spends a night at Rutgers University, a night at the University of Miami, and a night at Clemson University is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F120 ALIGN=MIDDLE  ALT=\"1%2F120\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "THE MATH TEACHER SAYS:<BR>\n" );
document.write( "This is a case of combinations (setof items, where order does not matter).<BR>\n" );
document.write( "The number of combinations of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > items taken without replacement from a set of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > items is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2Cn%2Cr%29%29=n%21%2F%28r%21%28n-r%29%21%29 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2Cn%2Cr%29%29=n%21%2F%28r%21%28n-r%29%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In this case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=10 ALIGN=MIDDLE  ALT=\"n=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=3 ALIGN=MIDDLE  ALT=\"r=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the number of possible sets of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > colleges where Anthony could spend the night,<BR>\n" );
document.write( "out of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > colleges he wanted to visit is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C10%2C3%29%29=10%21%2F%283%21%2810-3%29%21%29=10%21%2F%283%217%21%29=10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%2F%283%2A2%2A1%29%287%2A6%2A5%2A4%2A3%2A2%2A1%29%29=10%2A9%2A8%2Across%287%29%2Across%286%29%2Across%285%29%2Across%284%29%2Across%283%29%2Across%282%29%2Across%281%29%2F%283%2A2%2A1%2Across%287%29%2Across%286%29%2Across%285%29%2Across%284%29%2Across%283%29%2Across%282%29%2Across%281%29%29%29=720%2F6=120 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "{Rutgers U, U Miami, Clemson U} is one 3-college subset of the 10-college set of colleges that Anthony wants to visit.<BR>\n" );
document.write( "The probability that the set of 3 colleges where Anthony spends a night<BR>\n" );
document.write( "is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > particular set out of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120 ALIGN=MIDDLE  ALT=\"120\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible sets is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F120 ALIGN=MIDDLE  ALT=\"1%2F120\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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