document.write( "Question 1189702: 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?
\n" ); document.write( "a)96 b)120 c)144 d)180 e)240 \n" ); document.write( "

Algebra.Com's Answer #821157 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "The letters C,I,R,C,L, and E can be used to form 6-letter strings such as CIRCLE or CCIRLE.
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\n" ); document.write( "of the letter C are separated by at least one other letter?
\n" ); document.write( "a)96 b)120 c)144 d)180 e)240
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document.write( "(1)  From the context, it is clear that they want you consider only DISTINGUISHABLE strings.\r\n" );
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document.write( "(2)  In the word \"CIRCLE\", there are 6 letters; of them, letter C is of multiplicity 2.\r\n" );
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document.write( "     THEREFORE, the number of all possible distinguishable strings is   = 720/2 = 360.\r\n" );
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document.write( "(3)  Of them, the number of all distinguishable strings with two attached (glued) letters C is  (6-1)! = 5! = 120.\r\n" );
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document.write( "     These 120 strings are UNFAVORABLE.  The rest 360-120 = 240 distinguishable strings are favorable.\r\n" );
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document.write( "ANSWER.  There are 240 distinguishable strings, where two occurrences of the letter C are separated by at least one other letter.\r\n" );
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document.write( "         Option e)\r\n" );
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