document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199154>Question 1199154</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider all of the ways of ordering the 5 letters U,S,A,M,O. Suppose these are listed in a dictionary in alphabetical order, starting with AMOSU. What position In the list would USAMO be? \r<BR>\n" );
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document.write( "A. 97 B. 103 C. 109 D. 115 E. 120\r<BR>\n" );
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document.write( "(If your answer is not one of these answer choices, you should double check your work, as it is wrong.) </SPAN>\n" );
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document.write( "The number of arrangements of the 5 letters is 5! = 120.  We are looking for the position in an alphabetical list of the 120 arrangements of \"USAMO\".<br><BR>\n" );
document.write( "In the list of 120 arrangements, there are 4! = 24 arrangements starting with each letter.  Since U is the last of the 5 letters alphabetically, there are 4*24 = 96 arrangements in the list before the first one with first letter U.<br><BR>\n" );
document.write( "Given first letter U, there are 3! = 6 arrangements with each of the 4 second letters.  Among the letters S, A, M, and O, S is last alphabetically, so there are 3*6=18 arrangements with first letter U before the first one with second letter S.<br><BR>\n" );
document.write( "So, before the first arrangement with first two letters US, there are 96 + 18 = 114 arrangements.<br><BR>\n" );
document.write( "Among the 6 arrangements with first two letters US, the arrangement USAMO is first alphabetically, so the position in the list of USAMO is 114 + 1 = 115.<br><BR>\n" );
document.write( "ANSWER: 115<br><BR>\n" );
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