document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=419253>Question 419253</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with my math homework:<BR>\n" );
document.write( "1. A quiz consists of 5 multiple-choice questions, each has three possible answers. In how many different ways can the quiz be answered if an answer is chosen for each question?<BR>\n" );
document.write( "I said 5 x 3 = 15<BR>\n" );
document.write( "2. In how many ways can three different math books and four different English books be arranged in a row if the books for each subject are placed together?<BR>\n" );
document.write( "3 x 4 = 12<BR>\n" );
document.write( "3. In how many different ways can three finalists be selected from 15 job applicants for a second round interview?<BR>\n" );
document.write( "15 x 3 = 45<BR>\n" );
document.write( "4. Fifteen dogs enter a Goofy Dog contest. In how many different ways can a champion, a first runner-up, and a second runner-up be selected?<BR>\n" );
document.write( "15 x 3 = 45\r<BR>\n" );
document.write( "\n" );
document.write( "Is this correct? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293232 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=293232\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. A quiz consists of 5 multiple-choice questions, each has three possible answers. In how many different ways can the quiz be answered if an answer is chosen for each question?<BR>\n" );
document.write( "I said 5 x 3 = 15<BR>\n" );
document.write( "It's 3^5 = 243 possibilities.<BR>\n" );
document.write( "If the answers for each are A, B & C, you can have<BR>\n" );
document.write( "A A A A A<BR>\n" );
document.write( "A A A A B<BR>\n" );
document.write( "A A A A C<BR>\n" );
document.write( "A A A B A<BR>\n" );
document.write( "A A A B B<BR>\n" );
document.write( "A A A B C<BR>\n" );
document.write( "A A A C A<BR>\n" );
document.write( "A A A C B<BR>\n" );
document.write( "A A A C C<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "You can see there are more than 15.<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "2. In how many ways can three different math books and four different English books be arranged in a row if the books for each subject are placed together?<BR>\n" );
document.write( "3 x 4 = 12<BR>\n" );
document.write( "With the math books first, the 1st book can be 1 of 3, the 2nd 1 of 2, then 1<BR>\n" );
document.write( "= 3*2*1 = 6<BR>\n" );
document.write( "For the English books, it's 4*3*2 *1 = 24<BR>\n" );
document.write( "6*24 = 144<BR>\n" );
document.write( "Then the English books can be first, --> 288 ways.<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "3. In how many different ways can three finalists be selected from 15 job applicants for a second round interview?<BR>\n" );
document.write( "15 x 3 = 45<BR>\n" );
document.write( "It's 15*14*13 = 2730<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "4. Fifteen dogs enter a Goofy Dog contest. In how many different ways can a champion, a first runner-up, and a second runner-up be selected?<BR>\n" );
document.write( "15 x 3 = 45 <BR>\n" );
document.write( "Same as #3, 2730<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );