document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=717642>Question 717642</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose an exam has 34 questions on it and students need to answer 22 of the questions.  In how many ways<BR>\n" );
document.write( "can this be done if the first 4 and exactly 5 of the last 8 questions must be answered and question #13 must not <BR>\n" );
document.write( "be answered because of a typo?\r<BR>\n" );
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document.write( "Pilion Pizza makes a specialty pizza with 4 layers of toppings alternating with layers of cheese and <BR>\n" );
document.write( "advertises that it offers 36 different toppings.<BR>\n" );
document.write( "a)  How many different pizzas can be made if none of the toppings can be duplicated and the<BR>\n" );
document.write( "     order of the toppings matters?<BR>\n" );
document.write( "b)  How many different pizzas can be made if none of the toppings can be duplicated and the<BR>\n" );
document.write( "     order of the toppings doesn’t matter? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #440384 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=440384\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose an exam has 34 questions on it and students need to answer 22 of the questions. In how many ways can this be done if the first 4 and exactly 5 of the last 8 questions must be answered and question #13 must not <BR>\n" );
document.write( "be answered because of a typo?<BR>\n" );
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document.write( "# of ways to answer the first 4: 1<BR>\n" );
document.write( "# of ways to answer #13: 0<BR>\n" );
document.write( "# of ways to answer of the last 8: 8C5 = 56<BR>\n" );
document.write( "# of ways to answer 10 of the remaining 21: = 352716<BR>\n" );
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document.write( "Total # of ways : 1 * 56*352716 = 5643456<BR>\n" );
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document.write( "Pilion Pizza makes a specialty pizza with 4 layers of toppings alternating with (number missing here) layers of cheese and (?? here) advertises that it offers 36 different toppings.<BR>\n" );
document.write( "a) How many different pizzas can be made if none of the toppings can be duplicated and the<BR>\n" );
document.write( "order of the toppings matters?<BR>\n" );
document.write( "b) How many different pizzas can be made if none of the toppings can be duplicated and the<BR>\n" );
document.write( "order of the toppings doesn’t matter?\r<BR>\n" );
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document.write( "======<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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