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 #814197 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814197\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there is only one possible code.<BR>\n" );
document.write( "the possible digits are 2,4,6,8.<BR>\n" );
document.write( "can't be 0<BR>\n" );
document.write( "can't be any odd number between 0 and 9.<BR>\n" );
document.write( "the probability that the first digit is the right digit is 1/4.<BR>\n" );
document.write( "the probability that the second digit is the right digit, assuming that the the first digit is correct, is 1/3.<BR>\n" );
document.write( "the probability that the third digit is the right digit, assuming that the first two digits are correct, is 1/2.<BR>\n" );
document.write( "the total probability is 1/4 * 1/3 * 1/2 = 1/24.\r<BR>\n" );
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document.write( "if you look at the number of permutations possible, you will get 4P3 = 4! / (1!) = 4*3*2*1 / 1 = 24.\r<BR>\n" );
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document.write( "only one of those permutations is the correct permutation, therefore the probability is 1/24.\r<BR>\n" );
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document.write( "the permutation formula is p(n,x) = n! / (n-x)!.<BR>\n" );
document.write( "when n = 4 and x = 3, the formula becomes p(4,3) = 4! / (4-3)! = 4! / 1! = 24.\r<BR>\n" );
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document.write( "only one permutation out of those 24 permutations is the correct permutation,  therefore the probability is 1/24.\r<BR>\n" );
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document.write( "i'm pretty sure this is correct.<BR>\n" );
document.write( "i was able to get the same answer both ways.<BR>\n" );
document.write( "the denominator is the permutation of 4 possible numbers taken 3 at a time.<BR>\n" );
document.write( "the numerator is 1.<BR>\n" );
document.write( "the possible number are 2,4,6,8.\r<BR>\n" );
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document.write( "the possible 3 digit permutations are:\r<BR>\n" );
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document.write( "2 4 6 *****<BR>\n" );
document.write( "2 6 4<BR>\n" );
document.write( "4 2 6<BR>\n" );
document.write( "4 6 2<BR>\n" );
document.write( "6 2 4<BR>\n" );
document.write( "6 4 2\r<BR>\n" );
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document.write( "2 4 8 *****<BR>\n" );
document.write( "2 8 4<BR>\n" );
document.write( "4 2 8 <BR>\n" );
document.write( "4 8 2<BR>\n" );
document.write( "8 2 4<BR>\n" );
document.write( "8 4 2\r<BR>\n" );
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document.write( "2 6 8 *****<BR>\n" );
document.write( "2 8 6<BR>\n" );
document.write( "6 2 8<BR>\n" );
document.write( "6 8 2<BR>\n" );
document.write( "8 2 6<BR>\n" );
document.write( "8 6 2\r<BR>\n" );
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document.write( "4 6 8 *****<BR>\n" );
document.write( "4 8 6<BR>\n" );
document.write( "6 4 8<BR>\n" );
document.write( "6 8 4<BR>\n" );
document.write( "8 4 6<BR>\n" );
document.write( "8 6 4\r<BR>\n" );
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document.write( "note that you have 4 sets of 6 = 24.\r<BR>\n" );
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document.write( "each set of 6 is a separate combination, if you don't take order of the digits into account\r<BR>\n" );
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document.write( "the permutation formula is p(n,x) = n! / (n-x)!\r<BR>\n" );
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document.write( "the combination formula is c(n,x) = n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "when n = 4 and x = 3, these formulas become:\r<BR>\n" );
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document.write( "p(4,3) = 4! / 3! = 4! = 24.\r<BR>\n" );
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document.write( "c(4,3) = 4! / (3! * 1!) = 4! / 3! = 4.\r<BR>\n" );
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document.write( "you have 4 possible combinatins where order is not important.<BR>\n" );
document.write( "they are:\r<BR>\n" );
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document.write( "2 4 6<BR>\n" );
document.write( "2 4 8<BR>\n" );
document.write( "2 6 8<BR>\n" );
document.write( "4 6 8\r<BR>\n" );
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document.write( "within each of those you have 6 possible arrangements where order is important.\r<BR>\n" );
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document.write( "4 * 6 = 24.\r<BR>\n" );
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document.write( "he will need to try up to 24 possible permutations and is assured to get the right combination.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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