document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183743>Question 1183743</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am confused on how to solve this, may you please help?\r<BR>\n" );
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document.write( "Use a factorial, permutation or combination to find the probability of the given event. Do NOT simplify your answer. Only consider digits greater than zero.\r<BR>\n" );
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document.write( "Bill forgot the last three digits of his 8 digit password. He only remembers that the digits are even and not the same. What is the probability he enters the correct password on the first try? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814199 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The other tutor goes through a lengthy explanation of why there are only 24 possible sequences (permutations) of the last three digits, so that the probability of getting the right password on the first attempt is 1/24.<br><BR>\n" );
document.write( "That is quite possibly the answer the author of the problem wanted; however, grammatically it is not the right answer.<br><BR>\n" );
document.write( "The problem is with the phrasing of the question, which says the three last digits are \"even and not the same\".<br><BR>\n" );
document.write( "That does NOT mean the same thing as \"even and all different\".  For example, the digits 224 are all even and not the same....<br><BR>\n" );
document.write( "So with the way the problem is stated, the only sequences NOT allowed are 222, 444, 666, and 888.<br><BR>\n" );
document.write( "Without restrictions, the number of possible permutations of the last three digits is 4*4*4=64; with the 4 excluded ones, the number of allowable permutations is 64-4=60.  And of course only one of them is the correct one.<br><BR>\n" );
document.write( "ANSWER: The probability of entering the correct password on the first try is 1/60.<br><BR>\n" );
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