document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209361>Question 1209361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many values greater than 7000 can be formed using the digits 3, 5, 7, 8, 9 without repetition? </SPAN>\n" );
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document.write( "Consider four-digit numbers of the form ABCD where A,B,C,D represent digits chosen from {3,5,7,8,9} with no repeats allowed. <BR>\n" );
document.write( "The choices for A could be 7, 8 or 9 to ensure that the number exceeds 7000.<BR>\n" );
document.write( "So we have 3 choices for slot A.<BR>\n" );
document.write( "Whatever is selected for A, we have 4 choices for B, 3 for C, and 2 for D.<BR>\n" );
document.write( "It yields 3*4*3*2 = 72 different ways to create the four-digit numbers.\r<BR>\n" );
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document.write( "Now consider the five-digit case. Numbers will look like ABCDE<BR>\n" );
document.write( "Where A through E are chosen from {3,5,7,8,9} and no repeats are allowed. <BR>\n" );
document.write( "There are 5*4*3*2*1 = 120 possible five-digit values larger than 7000. <BR>\n" );
document.write( "Any permutation of these 5 digits will be larger than 7000 simply because any five-digit number is larger than any four-digit number.<BR>\n" );
document.write( "We cannot form six-digit numbers or larger since we only have 5 digits to work with and repeats aren't allowed.\r<BR>\n" );
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document.write( "We found there are 72 ways to form the four-digit numbers, and 120 ways to form the five-digit numbers, such that whatever formed is larger than 7000.\r<BR>\n" );
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document.write( "Therefore,<BR>\n" );
document.write( "72+120 = <font color=red>192</font> is the final answer.<BR>\n" );
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