document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1055966>Question 1055966</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ted has a cat carrier which will hold 3 cats. Unfortunately, Ted has 5 cats: Muffy, Nero, Oprah, Penny, and Quade.<BR>\n" );
document.write( "a. Make an organized list to show all the ways Ted can chose 3 cats at random to put in the cat carrier.  My answer: 5 x 4 x 3 = 60 I am not sure how to make a list.\r<BR>\n" );
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document.write( "b. How many of the ways in part (a) contain Oprah?<BR>\n" );
document.write( "c. How many ways in part (b) contain both Muffy and Nero.<BR>\n" );
document.write( "d. Based on your answers to parts (a) and (b) what is the probability that Oprah will end up in the cat carrier?\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 #671131 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=671131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let,<BR>\n" );
document.write( "M = Muffy<BR>\n" );
document.write( "N = Nero<BR>\n" );
document.write( "O = Oprah<BR>\n" );
document.write( "P = Penny<BR>\n" );
document.write( "Q = Quade\r<BR>\n" );
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document.write( "(a)\r<BR>\n" );
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document.write( "5*4*3 = 60\r<BR>\n" );
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document.write( "There are 60 ways to do this if order mattered, but it doesn't. So we divide by 6. Why 6? Because there are 6 ways to order any 3 individuals (3! = 3*2*1 = 6). \r<BR>\n" );
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document.write( "60/6 = 10\r<BR>\n" );
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document.write( "So the final answer to part (a) is <font color=red>10</font>. The list would be \r<BR>\n" );
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document.write( "M,N,O<BR>\n" );
document.write( "M,N,P<BR>\n" );
document.write( "M,N,Q<BR>\n" );
document.write( "M,O,P<BR>\n" );
document.write( "M,O,Q<BR>\n" );
document.write( "M,P,Q<BR>\n" );
document.write( "N,O,P<BR>\n" );
document.write( "N,O,Q<BR>\n" );
document.write( "N,P,Q<BR>\n" );
document.write( "O,P,Q\r<BR>\n" );
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document.write( "each line represents a different combination. Something like M,N,O is the same as M,O,N or N,M,O since they have the same 3 cats just in a different order. Order does not matter. As you can see in the list above, there are 10 different combinations. \r<BR>\n" );
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document.write( "(b)\r<BR>\n" );
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document.write( "Hold one slot to have it fill Oprah (O). There are 2 slots left with 4 choices to fill it\r<BR>\n" );
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document.write( "4 C 2 = (4 P 2)/(2!) = (4*3)/2 = 12/2 = 6\r<BR>\n" );
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document.write( "There are 6 ways to do this\r<BR>\n" );
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document.write( "If you look at the list in part (a), you'll see these entries that have O in them somehow\r<BR>\n" );
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document.write( "M,N,O<BR>\n" );
document.write( "M,O,P<BR>\n" );
document.write( "M,O,Q<BR>\n" );
document.write( "N,O,P<BR>\n" );
document.write( "N,O,Q<BR>\n" );
document.write( "O,P,Q\r<BR>\n" );
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document.write( "There are 6 of those entries listed above. So however you do it, the final answer to part (b) is <font color=red>6</font>\r<BR>\n" );
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document.write( "(c)\r<BR>\n" );
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document.write( "Look at the list in part (b). Look for entries that have both M and N together at the same time. It only happens once and it is M,N,O\r<BR>\n" );
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document.write( "The final answer to part (c) is <font color=red>1</font>\r<BR>\n" );
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document.write( "(d)\r<BR>\n" );
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document.write( "In part (a), the answer is 10<BR>\n" );
document.write( "In part (b), the answer is 6\r<BR>\n" );
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document.write( "There are 6 ways to get what we want (have Oprah picked) out of 10 ways total\r<BR>\n" );
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document.write( "Simply divide the two values to get\r<BR>\n" );
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document.write( "6/10 = 3/5 = 0.6\r<BR>\n" );
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document.write( "The final answer as a fraction is <font color=red>3/5</font>. Don't forget to reduce fully.\r<BR>\n" );
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document.write( "The final answer in decimal form is <font color=red>0.6</font>\r<BR>\n" );
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document.write( "The final answer as a percentage is <font color=red>60%</font>\r<BR>\n" );
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document.write( "The way you report the answer will depend on your teacher's instructions.  </SPAN>\n" );
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