document.write( "Question 1150816: The problem is: Find the number of ways in which four girls and three boys can
\n" ); document.write( "arrange themselves in a row so that none of the boys are together?\r
\n" ); document.write( "\n" ); document.write( "There are two possible solutions but only one is considered.\r
\n" ); document.write( "\n" ); document.write( "The first one, in which I made, is that, we can lay the three boys firstly in
\n" ); document.write( "the row, making it _B1_B2_B3_. Since there are 4 spaces, in each space we can
\n" ); document.write( "permute the girls. Thus the solution is 4!*3!=144 ways\r
\n" ); document.write( "\n" ); document.write( "Now the second one, we can lay the four girls before the boys, leaving blank
\n" ); document.write( "spaces for the boys at this configuration: _G_G_G_G_. Since there are 5 blanks,
\n" ); document.write( "boys can choose their positions giving it a 5P3. By multiplication, the answer
\n" ); document.write( "is 5P3*4!=1440 ways\r
\n" ); document.write( "\n" ); document.write( "And to conclude, the right answer,at most it would be considered,is the second
\n" ); document.write( "one, 1440 ways. My question is why the first one is not the right answer? At
\n" ); document.write( "what fair reason should it be accounted? Did I undercount, and/or make a gap in
\n" ); document.write( "my logic? Hope to shed a clear explanation on my question. Thank you.
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Algebra.Com's Answer #772303 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Your first answer is incorrect because 144 is the number of ways none of the boys\r\n" );
document.write( "AND NONE OF THE GIRLS are together.  But it was not\r\n" );
document.write( "required that none of the girls could be together.\r\n" );
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document.write( "Edwin
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