document.write( "Question 1149531: In how many ways can 3 boys and 2 girls be arranged in a row if a selection is made from 5 boys and 4 girls? In how many of these arrangements does a boy occupy the middle position? \n" ); document.write( "

Algebra.Com's Answer #770909 by Edwin McCravy(20054) $\"\"$ $\"About$

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In how many ways can 3 boys and 2 girls be arranged in a row if a selection
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document.write( "Choose the boys 5C3 ways\r\n" );
document.write( "Choose the girls 4C2 ways\r\n" );
document.write( "Place the boys in 5P3 ways\r\n" );
document.write( "Place the girls in 2P2 ways\r\n" );
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document.write( "(5C3)(4C2)(5P3)(2P2) = (10)(6)(60)(2) = 7200 ways.\r\n" );
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In how many of these arrangements does a boy occupy the middle position?

Choose the boy to occupy the middle position in 5C1 ways.\r\n" );
document.write( "That leaves 4 positions to be filled with 2 boys and 2 girls\r\n" );
document.write( "[from 4 remaining boys and 4 girls]\r\n" );
document.write( "Choose the boys 4C2 ways\r\n" );
document.write( "Choose the girls 4C2 ways\r\n" );
document.write( "Place the 2 chosen boys in 2 of the 4 empty seats 4P2 ways\r\n" );
document.write( "Place the 2 chosen girls in the remaining 2 empty seats 2P2 ways \r\n" );
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document.write( "(5C1)(4C2)(4C2)(4P2)(2P2) = (5)(6)(6)(12)(2) = 4320 ways.\r\n" );
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document.write( "Edwin

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