document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1041970>Question 1041970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Five students will be randomly selected from the seven top students in mathematics to represent their school in a regional competition. Angela (A) and Brian (B) are among the seven students, and they wish to determine the probability that they will both be chosen. Using A, B, C, D, E, F, and G to denote the students, set up a sample space to determine this probability. What is the probability they will both be chosen? Enter probability as a fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #657293 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=657293\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at the number of possible choices that contain both A and B, that leaves 3 choices to pick out of a pool of 5.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=C%285%2C3%29=10 ALIGN=MIDDLE  ALT=\"N=C%285%2C3%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For the sample space, look at all possible 3 pick choices not including A and B.<BR>\n" );
document.write( "ABCDE, ABCDF, ABCDG<BR>\n" );
document.write( "ABCEF, ABCEG<BR>\n" );
document.write( "ABCFG<BR>\n" );
document.write( "ABDEF, ABDEG<BR>\n" );
document.write( "ABDFG<BR>\n" );
document.write( "ABEFG<BR>\n" );
document.write( "Look at the total number of possible choices, 5 choices out of a pool of 7.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N%5BTOT%5D=C%287%2C5%29=21 ALIGN=MIDDLE  ALT=\"N%5BTOT%5D=C%287%2C5%29=21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then the probability would be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=N%2FN%5BTOT%5D=10%2F21 ALIGN=MIDDLE  ALT=\"P=N%2FN%5BTOT%5D=10%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "ABCDE, ABCDF, ABCDG, ABCEF, ABCEG, ABCFG<BR>\n" );
document.write( "ABDEF, ABDEG, ABDFG<BR>\n" );
document.write( "ABEFG<BR>\n" );
document.write( "ACDEF, ACDEG, ACDFG, <BR>\n" );
document.write( "ACEFG<BR>\n" );
document.write( "ADEFG<BR>\n" );
document.write( "BCDEF, BCDEG, BCDFG<BR>\n" );
document.write( "BCEFG<BR>\n" );
document.write( "BDEFG<BR>\n" );
document.write( "CDEFG<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );