document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193982>Question 1193982</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A photograph of a diving team is to be taken with the team members in two rows. The team has four girls and two boys. The back row has four places while the front row has the coach in the middle with one diver to the left and one diver to the right. How many ways can the divers be arranged in the photograph if the boys and girls are to alternate in the back row? \r<BR>\n" );
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document.write( "The textbook answer is 96. \r<BR>\n" );
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document.write( "Can someone explain the solution of this problem? Thanks.  </SPAN>\n" );
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document.write( "(1) The back row must contain both boys and 2 of the 4 girls.  We need to choose 2 of the 4 girls to be in the back row.  The number of ways to do that is C(4,2) = 6.<br><BR>\n" );
document.write( "(2) We need to arrange the 4 people in the back row so that boys and girls alternate.<BR>\n" );
document.write( "The first person in the row can be any of the 4<BR>\n" );
document.write( "The second person must be one of the 2 of the opposite gender<BR>\n" );
document.write( "The third person has to be the other student of the same gender as the first<BR>\n" );
document.write( "The fourth person has to be the other student of the same gender as the second<br><BR>\n" );
document.write( "Number of ways to arrange the 4 people in the back row: 4*2*1*1 = 8<br><BR>\n" );
document.write( "(3) The two girls in the front row can be arranged in 2 different ways.<br><BR>\n" );
document.write( "Total number of ways to arrange the students in the photograph: 6*8*2 = 96<br><BR>\n" );
document.write( "ANSWER: 96<br><BR>\n" );
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