document.write( "Question 1063535: In a row of 6 counters, 3 are red, 2 are blue and 1 is white.
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Algebra.Com's Answer #678782 by Edwin McCravy(20055) $\"\"$ $\"About$

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In a row of 6 counters, 3 are red, 2 are blue and 1 is white.
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\n" ); document.write( "next to another red counter.
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document.write( "I will assume that the counters of the same color cannot be told apart,\r\n" );
document.write( "i.e., are indistinguishable.  If this is a false assumption, and they are\r\n" );
document.write( "to be considered as distinguishable, then tell me in the thank-you note \r\n" );
document.write( "form below and I'll get back to you by email. (No charge ever, as I do \r\n" );
document.write( "this for fun and to help you).\r\n" );
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document.write( "First we place the non-red ones any of these 3C1 = 3 ways:\r\n" );
document.write( "[(3 places choose 1) ways to place the white one.  The\r\n" );
document.write( "3 ways are \r\n" );
document.write( "1. right of, \r\n" );
document.write( "2. between, and \r\n" );
document.write( "3. left of the two blue ones.\r\n" );
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document.write( "             B B W\r\n" );
document.write( "             B W B\r\n" );
document.write( "             W B B\r\n" );
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document.write( "Then for each of these ways of arranging the 3 non-red ones, there\r\n" );
document.write( "are 4 places to put the 3 red ones:\r\n" );
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document.write( "1. to the left of the left-most non-red one.\r\n" );
document.write( "2. between the left-most non-red one and the middle non-red one.\r\n" );
document.write( "3. between the middle non-red one and the right-most non-red one.\r\n" );
document.write( "4. to the right of the right-most non-red one.\r\n" );
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document.write( "That's (3C1)(4C3) = (3)(4) = 12 ways.\r\n" );
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document.write( "The 12 ways are:\r\n" );
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document.write( " 1.  RBRBRW\r\n" );
document.write( " 2.  RBRBWR\r\n" );
document.write( " 3.  RBBRWR\r\n" );
document.write( " 4.  BRBRWR\r\n" );
document.write( " 5.  RBRWRR\r\n" );
document.write( " 6.  RBRWRR\r\n" );
document.write( " 7.  RBWRRR\r\n" );
document.write( " 8.  BRWRRR\r\n" );
document.write( " 9.  RWRBRB\r\n" );
document.write( "10.  RWRBBR\r\n" );
document.write( "11.  RWBRBR\r\n" );
document.write( "12.  WRBRBR\r\n" );
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document.write( "Be sure to let me know if the counters are distinguishable.\r\n" );
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document.write( "Edwin

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