document.write( "Question 1031493: The total number of ways in which six + and four - signs can be arranged in a line such that no two - signs occur together is
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\n" ); document.write( "c)35(correct)
\n" ); document.write( "d)none of these \n" ); document.write( "
Algebra.Com's Answer #646206 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We only need three of the + signs to keep two of the \r\n" );
document.write( "4 - signs from coming together, like this:\r\n" );
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document.write( " - + - + - + -\r\n" );
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document.write( "Now we must insert the remaining three + signs\r\n" );
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document.write( "The arrows below point to the 5 places where we may insert \r\n" );
document.write( "the remaining 3 + signs:\r\n" );
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document.write( "↓   ↓   ↓   ↓ ↓ \r\n" );
document.write( " - + - + - + -\r\n" );
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document.write( "The 5 places are:\r\n" );
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document.write( "Left of the 1st - sign\r\n" );
document.write( "Immediate left of the 2nd - sign\r\n" );
document.write( "Immediate left of the 3rd - sign\r\n" );
document.write( "Immediate left of the 4th - sign\r\n" );
document.write( "Right of the 4th - sign \r\n" );
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document.write( "Case 1:  We put all three +++ in one of the 5 places:\r\n" );
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document.write( "That's 5 ways.\r\n" );
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document.write( "+++-+-+-+-\r\n" );
document.write( "-++++-+-+-\r\n" );
document.write( "-+-++++-+-\r\n" );
document.write( "-+-+-++++-\r\n" );
document.write( "-+-+-+-+++\r\n" );
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document.write( "Case 2: We put a pair ++ in one of the 5 places and \r\n" );
document.write( "a single + in another\r\n" );
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document.write( "We can choose the place to put the pair ++ in 5 ways\r\n" );
document.write( "and there remain 4 ways we can choose the place to put \r\n" );
document.write( "the single +.\r\n" );
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document.write( "That's 5*4 = 20 ways.\r\n" );
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document.write( "Case 3:  We place a single + in 3 different places.\r\n" );
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document.write( "We can choose the 3 places to put the 3 single +'s\r\n" );
document.write( "in 5C3 = 10 ways.\r\n" );
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document.write( "Grand total: 5+20+10 = 35 ways.  \r\n" );
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document.write( "Edwin

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