document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189433>Question 1189433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the probability that a random arrangement of the letters in the word `SEVEN' will have both E's next to each other?<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 #820791 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=820791\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Edit: I corrected the final answer to have it fully reduced. I appreciate @greenestamps pointing out the error.\r<BR>\n" );
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document.write( "If we could tell the two \"E\"s apart, then there would be 5! = 5*4*3*2*1 = 120 permutations of the word SEVEN since there are 5 letters.\r<BR>\n" );
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document.write( "However, we cannot tell the \"E\"s apart. This means we've double-counted when computing that figure of 120. So we must cut that figure in half to get 60.\r<BR>\n" );
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document.write( "There are 60 ways to arrange the letters of SEVEN where the \"E\"s may or may not be together.\r<BR>\n" );
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document.write( "Let's take the \"E\"s out and replace it with some other letter. I'll use W. <BR>\n" );
document.write( "So we go from the word SEVEN to the \"word\" SWVN\r<BR>\n" );
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document.write( "There are 4 distinct letters here, so there are 4! = 4*3*2*1 = 24 permutations. Anywhere you see a W, replace it with EE\r<BR>\n" );
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document.write( "A permutation like WSVN is really EESVN<BR>\n" );
document.write( "A permutation like SVWN is really SVEEN<BR>\n" );
document.write( "and so on.\r<BR>\n" );
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document.write( "We found that there are:<ul><li>24 ways to arrange the letters so the \"E\"s are together</li><li>60 ways to arrange the letters overall</li></ul> Divide the two values to get: 24/60 = (12*2)/(12*5) = 2/5\r<BR>\n" );
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document.write( "<font color=red>Answer: 2/5</font><BR>\n" );
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