document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203178>Question 1203178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a certain school, the principal gave the analysis of the qualified subject teachers in the school as follows:<BR>\n" );
document.write( "English teachers = 10<BR>\n" );
document.write( "Biology teachers = 12<BR>\n" );
document.write( "French teachers = 6<BR>\n" );
document.write( "Mathematics teachers = 8<BR>\n" );
document.write( "Physics teachers = 4<BR>\n" );
document.write( "If two teachers are to represent the school in a workshop, what is the probability that both will come from either Biology or Physics?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838533 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838533\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "NOTE: There are two interpretations of the problem.<BR>\n" );
document.write( "(1) both are biology teachers or both are physics teachers<BR>\n" );
document.write( "(2) both are either biology teachers or physics teachers<br><BR>\n" );
document.write( "Total number of teachers: 10+12+6+8+4 = 40<br><BR>\n" );
document.write( "Number of ways of choosing 2 teachers: \"40 choose 2\" = C(40,2) = (40*39)/(2*1) = 780<br><BR>\n" );
document.write( "Number of ways of choosing 2 biology teachers: 12 choose 2 = C(12,2) = (12*11)/(2*1) = 66<br><BR>\n" );
document.write( "Number of ways of choosing 2 physics teachers: 4 choose 2 = C(4,2) = (4*3)/(2*1) = 6<br><BR>\n" );
document.write( "ANSWER: probability that either 2 biology or 2 physics teachers are selected = (66+6)/780 = 72/780 = 6/65<br><BR>\n" );
document.write( "With the other interpretation, the number of ways of selecting two teachers who are EITHER biology or physics teachers is<br><BR>\n" );
document.write( "C(16,2)/C(40,2) = 120/780 = 2/13<br> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );