document.write( "Question 1022916: Ten distinguishable balls are distributed into 4 distant boxes such that a specified box contains exactly 2 balls.Find number of such distribution ?
\n" ); document.write( "A.3 power 8 B. 3 power 10
\n" ); document.write( "C.3 power 6. D.45*3 power 8
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Algebra.Com's Answer #638491 by Edwin McCravy(20055) $\"\"$ $\"About$

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Ten distinguishable balls are distributed into 4 distant boxes such that a specified box contains exactly 2 balls.Find number of such distribution ?
\n" ); document.write( "A.3 power 8 B. 3 power 10
\n" ); document.write( "C.3 power 6. D.45*3 power 8\r
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document.write( "We can choose the 2 balls to go in the specified box in 10C2 = 45 ways.\r\n" );
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document.write( "For every way that can be done, there are 8 balls left to \r\n" );
document.write( "distribute among the other 3 boxes.\r\n" );
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document.write( "There are 3 decisions to make for each remaining ball. \r\n" );
document.write( "Those 3 decisions are whether:\r\n" );
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document.write( "1. to place it in the first box, or\r\n" );
document.write( "2. to place it in the second box, or\r\n" );
document.write( "3. to place it in the third box.\r\n" );
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document.write( "So we have 3 possible decisions for the 1st remaining ball.\r\n" );
document.write( "And for each of those,\r\n" );
document.write( "we have 3 possible decisions for the 2nd remaining ball.\r\n" );
document.write( "And for each of those,\r\n" );
document.write( "we have 3 possible decisions for the 3rd remaining ball.\r\n" );
document.write( "And for each of those,\r\n" );
document.write( "we have 3 possible decisions for the 4th remaining ball.\r\n" );
document.write( "And for each of those,\r\n" );
document.write( "we have 3 possible decisions for the 5th remaining ball.\r\n" );
document.write( "And for each of those,\r\n" );
document.write( "we have 3 possible decisions for the 6th remaining ball.\r\n" );
document.write( "And  for each of those,\r\n" );
document.write( "we have 3 possible decisions for the 7th remaining ball.\r\n" );
document.write( "And  for each of those,\r\n" );
document.write( "we have 3 possible decisions for the 8th remaining ball.\r\n" );
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document.write( "So the answer is 45*3*3*3*3*3*3*3*3 = 45*3^8\r\n" );
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document.write( "Note: This allows the cases when some of the boxes are empty,\r\n" );
document.write( "and even some cases where all the remaining balls are all in \r\n" );
document.write( "one box.\r\n" );
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document.write( "Edwin

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