document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144351>Question 1144351</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You want to make five-letter codes that use the letters A, F, E, R, and M without repeating any letter. What is the probability that a randomly chosen code starts with M and ends with E?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #765441 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=765441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The total number of codes that can be formed of five different symbols that are not repeated in any valid code is the number of permutations of five things taken five at a time, to wit: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 5!\ =\ 5\ \times\ 4\ \times\ 3\ \times\ 2\ \times\ 1\"> because there are 5 ways to pick the first letter, and for each of those ways, there are 4 ways to pick the second letter making 20 ways to pick the first two letters. Then, for each of those 20 ways, there are 3 ways to pick the third letter, and so on.\r<BR>\n" );
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document.write( "The number of codes that start with one particular symbol and ends with a particular symbol is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 1\ \times\ 3\ \times\ 2\ \times\ 1\ \times\ 1\">.\r<BR>\n" );
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document.write( "The probability of any event is the number of successful outcomes divided by the number of total outcomes, or, in this case, the number of codes beginning and ending as specified divided by the total number of possible codes.   <BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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