Question 1189702
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The letters C,I,R,C,L, and E can be used to form 6-letter strings such as CIRCLE or CCIRLE. 
Using these letters, how many different 6-letter strings can be formed in which the two occurrences 
of the letter C are separated by at least one other letter?
a)96 b)120 c)144 d)180 e)240
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<pre>
(1)  From the context, it is clear that they want you consider only DISTINGUISHABLE strings.



(2)  In the word "CIRCLE", there are 6 letters; of them, letter C is of multiplicity 2.

     THEREFORE, the number of all possible distinguishable strings is  {{{6!/2!)}}} = 720/2 = 360.



(3)  Of them, the number of all distinguishable strings with two attached (glued) letters C is  (6-1)! = 5! = 120.

     These 120 strings are UNFAVORABLE.  The rest 360-120 = 240 distinguishable strings are favorable.



<U>ANSWER</U>.  There are 240 distinguishable strings, where two occurrences of the letter C are separated by at least one other letter.

         Option e)
</pre>

Solved and explained.