document.write( "Question 331658: Number of ways in which p positive and n negative signs may be placed in a row so that no two negative signs shall be together ?.\r
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Algebra.Com's Answer #237752 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "Number of ways in which p positive and n negative signs may be placed in a row\r\n" );
document.write( "so that no two negative signs shall be together ?.  More than an answer, I need\r\n" );
document.write( "the reasoning behind the answer. \r\n" );
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document.write( "Suppose you have p=10 positive signs and n=4 negative signs:\r\n" );
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document.write( "   +   +   +   +   +   +   +   +   +   +\r\n" );
document.write( " 1   2   3   4   5   6   7   8   9  10   11\r\n" );
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document.write( "Since negative signs cannot come together, we can only put one negative\r\n" );
document.write( "sign before any of the 10 positive signs, plus we can also place a negative\r\n" );
document.write( "sign after the 10th positive sign.  So there are 11 places we can insert a\r\n" );
document.write( "negative sign, and we must choose 4 of those to place the 4 negative signs:\r\n" );
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document.write( "So the answer for this specific case is 11C4\r\n" );
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document.write( "The reasoning is the same for any number p of positive signs and any number\r\n" );
document.write( "n of negative signs.  We can only put one negative sign before any of the p\r\n" );
document.write( "positive signs, plus we can also place a negative sign after the pth positive\r\n" );
document.write( "sign.  So there are p+1 places we can insert a negative sign, and we must\r\n" );
document.write( "choose n of those to place the n negative signs:\r\n" );
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document.write( "So the answer is \"(p+1) choose n\" which is also called \"the number of\r\n" );
document.write( "combinations of p+1 things taken n at a time\".\r\n" );
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document.write( "It is sometimes written , sometimes written  and sometimes written \r\n" );
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document.write( "It is calculated as \r\n" );
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document.write( "You need not worry if you have too many negative signs, i.e., if n > p+1,\r\n" );
document.write( "for the number of combinations is always defined as 0 in those cases.\r\n" );
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document.write( "Edwin

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