document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194074>Question 1194074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Four girls and three boys are seated randomly in a row. Calculate the following probabilities.<BR>\n" );
document.write( "(a) The girls occupy the first three places.<BR>\n" );
document.write( "(b) They are arranged to alternate girl, boy, girl, etc. \r<BR>\n" );
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document.write( "Answers<BR>\n" );
document.write( "(a) 4/35<BR>\n" );
document.write( "(b) 1/35\r<BR>\n" );
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document.write( "Can someone explain the answers? Thank you.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #826174 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=826174\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The solution from the other tutor is one standard way of answering these two questions.  You should understand it and be able to use it to solve similar problems.<br><BR>\n" );
document.write( "Another standard way of solving these problems is to consider the probabilities of filling the seats one at a time under the given constraints.<br><BR>\n" );
document.write( "(1) girls in first three places...<br><BR>\n" );
document.write( "first place: 7 people to choose from; 4 are girls --> P = 4/7<BR>\n" );
document.write( "second place: 6 people to choose from; 3 are girls --> P = 3/6<BR>\n" );
document.write( "third place: 5 people to choose from; 2 are girls --> P = 2/5<br><BR>\n" );
document.write( "P(girls in first three places) = (4/7)(3/6)(2/5) = 4/35<br><BR>\n" );
document.write( "(2) alternating...<br><BR>\n" );
document.write( "Obviously a girl must be first, then a boy, and so on.  Without showing in words the probabilities for getting the right gender in the right seat...<br><BR>\n" );
document.write( "P(alternating) = (4/7)(3/6)(3/5)(2/4)(2/3)(1/2)(1/1) = 1/35<br>\r<BR>\n" );
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