document.write( "Question 1146101: A school teacher has 6 girls and 8 boys to arrange for a choir. Determine the number of different ways she can arrange the 14 different children,\r
\n" ); document.write( "\n" ); document.write( "a)if the boys should stand behind the girls.
\n" ); document.write( "b)in a single row,if the girls must be kept together.
\n" ); document.write( "c)in a single row,if no two girls should stand next to each other.\r
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Algebra.Com's Answer #767482 by Edwin McCravy(20077)\"\" \"About 
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A school teacher has 6 girls and 8 boys to arrange for a choir. Determine the number of different ways she can arrange the 14 different children,
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document.write( "Answer = (8!)(6!) = (40320)(720) = 29030400 ways\r\n" );
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\n" ); document.write( "b)in a single row,if the girls must be kept together.
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document.write( "For each of the 6!=720 arrangements of the girls, there are\r\n" );
document.write( "9 things to arrange, (that is, 8 boys and 1 row of girls)\r\n" );
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document.write( "Answer = (6!)(9!) = (720)(362880) = 261273600\r\n" );
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\n" ); document.write( "c)in a single row,if no two girls should stand next to each other.
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document.write( "First we stand the boys in 8!=40320 ways\r\n" );
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document.write( " B B B B B B B B\r\n" );
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document.write( "We put a blank for each place a girl could be inserted between two boys\r\n" );
document.write( "or on one of the ends\r\n" );
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document.write( "Of those 10 places between two boys or on an end, we choose 6.\r\n" );
document.write( "So there are 10C6 = 210.\r\n" );
document.write( "For each of those 210 ways to place the 6 girls, they can be arranged in \r\n" );
document.write( "6!=720 ways.\r\n" );
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document.write( "Answer = 8!∙10C6∙6! = (40320)(210)(720) = 6096384000 ways.\r\n" );
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document.write( "Edwin
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