document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201073>Question 1201073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A corporation must appoint a president, chief executive officer (CEO), chief financial officer (CFO) and chief operating officer (COO). It must also appoint a planning committee with six different members.  There are 12 qualified candidates, and officers can also serve on the committee.\r<BR>\n" );
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document.write( "(i)	How many different ways can the officers be appointed?<BR>\n" );
document.write( "(ii)	What is the probability of randomly selecting the officers and getting the youngest candidate a president?<BR>\n" );
document.write( "(iii)	How many different ways can the committee be appointed?<BR>\n" );
document.write( "(iv)	What is the probability of randomly selecting the committee members and getting the six youngest of the qualified candidates?<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 #848045 by </B><A HREF=/tutors/aboutme.mpl?userid=asinus><B>asinus(45)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=asinus><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=848045\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Certainly, let's break down the calculations for each part:\r<BR>\n" );
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document.write( "**i) How many different ways can the officers be appointed?**\r<BR>\n" );
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document.write( "* We have 12 candidates for 4 positions: President, CEO, CFO, and COO. <BR>\n" );
document.write( "* The order of selection matters. <BR>\n" );
document.write( "* This is a permutation problem.\r<BR>\n" );
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document.write( "* Number of ways to appoint officers = 12P4 = 12! / (12-4)! = 12! / 8! = 12 * 11 * 10 * 9 = 11,880 ways\r<BR>\n" );
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document.write( "**ii) What is the probability of randomly selecting the officers and getting the youngest candidate a president?**\r<BR>\n" );
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document.write( "* There is only 1 youngest candidate.<BR>\n" );
document.write( "* For the President position, there is 1 favorable outcome (youngest candidate) out of 12 possible candidates.<BR>\n" );
document.write( "* For the other 3 positions (CEO, CFO, COO), there are no restrictions.\r<BR>\n" );
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document.write( "* Probability = (1/12) * (11/11) * (10/10) * (9/9) = 1/12\r<BR>\n" );
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document.write( "**iii) How many different ways can the committee be appointed?**\r<BR>\n" );
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document.write( "* We need to select 6 members out of 12 candidates.<BR>\n" );
document.write( "* The order of selection does not matter.<BR>\n" );
document.write( "* This is a combination problem.\r<BR>\n" );
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document.write( "* Number of ways to appoint the committee = 12C6 = 12! / (6! * (12-6)!) = 12! / (6! * 6!) = 924 ways\r<BR>\n" );
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document.write( "**iv) What is the probability of randomly selecting the committee members and getting the six youngest of the qualified candidates?**\r<BR>\n" );
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document.write( "* There is only 1 favorable outcome (selecting the 6 youngest candidates) out of 924 possible combinations.\r<BR>\n" );
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document.write( "* Probability = 1/924\r<BR>\n" );
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document.write( "Let me know if you have any other questions or would like to explore different scenarios! <BR>\n" );
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