document.write( "Question 802420: In how many ways can six girls and two boys be re arranged in a row (1) witout ristriction (2) such that the boys are not together. \n" ); document.write( "
Algebra.Com's Answer #483873 by Edwin McCravy(20060)\"\" \"About 
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document.write( "In how many ways can six girls and two boys be rearranged in a row. \r\n" );
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document.write( "(1) without ristriction \r\n" );
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document.write( "Choose the 1st person as any of the 8 people\r\n" );
document.write( "Choose the 2nd person as any of the 7 remaining unchosen people.\r\n" );
document.write( "Choose the 3rd person as any of the 6 remaining unchosen people.\r\n" );
document.write( "Choose the 4th person as any of the 5 remaining unchosen people.\r\n" );
document.write( "Choose the 5th person as any of the 4 remaining unchosen people.\r\n" );
document.write( "Choose the 6th person as any of the 3 remaining unchosen people.\r\n" );
document.write( "Choose the 7th person as either of the 2 remaining unchosen people.\r\n" );
document.write( "Choose the 8th person as the only 1 remaining unchosen person.\r\n" );
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document.write( "8*7*6*5*4*3*2*1 = 8! = 40320 ways\r\n" );
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document.write( "(2) such that the boys are not together.\r\n" );
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document.write( "From the 40320 from part (1) we must subtract the number of ways\r\n" );
document.write( "the boys can be together.  They can be considered as a \"pair of boys\"\r\n" );
document.write( "in 2 ways, with Tom on Dick's left, and with Dick on Tom's left.\r\n" );
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document.write( "With Tom on Dick's left:\r\n" );
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document.write( "As above except now we have 7 \"things\" to arrange,\r\n" );
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document.write( "6 girls and 1 \"pair of boys\".\r\n" );
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document.write( "That will be 7*6*5*4*3*2*1 = 7! = 5040 ways.\r\n" );
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document.write( "With Dick on Tom's left:\r\n" );
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document.write( "That's also 5040 ways.\r\n" );
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document.write( "So that's 2*5040 or 10080 to subtract from the 40320.\r\n" );
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document.write( "40320 - 10080 = 30240 ways. \r\n" );
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document.write( "Edwin
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