Question 1189433
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Edit: I corrected the final answer to have it fully reduced. I appreciate @greenestamps pointing out the error.


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.


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.


There are 60 ways to arrange the letters of SEVEN where the "E"s may or may not be together.


Let's take the "E"s out and replace it with some other letter. I'll use W. 
So we go from the word SEVEN to the "word" SWVN


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


A permutation like WSVN is really EESVN
A permutation like SVWN is really SVEEN
and so on.


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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



<font color=red>Answer: 2/5</font>
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