document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1188415>Question 1188415</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A committee of four is to be selected from a group of twenty people. How many different committees are possible, given the following conditions?<BR>\n" );
document.write( "One person is the chair, one person is the secretary, and the other two are responsible for refreshment clean up. </SPAN>\n" );
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document.write( "Let's focus on the first two slots for now. The order matters because the chairperson is different from the secretary. \r<BR>\n" );
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document.write( "We have 20 choices for the chairperson, then 19 choices for the secretary. That yields 20*19 = 380 permutations. Each time we arrive at a new seat, we count down by 1. Let A = 380 since we'll use it later.\r<BR>\n" );
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document.write( "Once we've filled those two slots, we have two additional seats where order does <u>not</u> matter. Both refreshment cleanup people have the same role/job. \r<BR>\n" );
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document.write( "We have 18 choices for the third slot and 17 choices for the fourth slot. That gives 18*17 = 306 permutations. However, order doesn't matter so we divide by 2 to get 306/2 = 153. This represents the number of ways to pick the remaining two spots on the committee. Let B = 153.\r<BR>\n" );
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document.write( "Overall, we have A*B = 306*153 = 58140 different ways to select the four person committee.\r<BR>\n" );
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document.write( "Answer: 58140<BR>\n" );
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