document.write( "Question 548199: total number of ways in which six 't' and four '-' signs can be arranged in a line such that no two '-' signs occur together is ? \n" ); document.write( "

Algebra.Com's Answer #356795 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "Let's examine a random arrangement of 6 \"t\"s and 4 \"-\"s:\r\n" );
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document.write( "Suppose we look at this arbitrary arrangement:\r\n" );
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document.write( "-  -  t  t  -  t  t  t  -  t\r\n" );
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document.write( "Let's number the positions:\r\n" );
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document.write( "1  2  3  4  5  6  7  8  9 10\r\n" );
document.write( "-  -  t  t  -  t  t  t  -  t\r\n" );
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document.write( "Notice that there are 10 positions. This particular one \r\n" );
document.write( "chooses positions 1,2,5, and 9 for the \"-\"s and the\r\n" );
document.write( "rest has \"t\"'s \r\n" );
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document.write( "So there are 10 positions, and we choose 4 of them\r\n" );
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document.write( "to put the -'s.  That's \"10 choose 4\" or 10C4 or C(10,4) or\r\n" );
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document.write( " =  = 210 ways\r\n" );
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document.write( "Edwin

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