document.write( "Question 1140056: in how many ways 5 different objects can be distributed among 3 persons so that exactly one person receives no object \n" ); document.write( "

Algebra.Com's Answer #760534 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Let the three persons be A, B and C.\r
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\n" ); document.write( "\n" ); document.write( "Case 1. The person A receives nothing.\r
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document.write( "    Then the person B receives some subset of 5 different objects, and the person C receives the rest \r\n" );
document.write( "    (receives the complement to the set that B receives).\r\n" );
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document.write( "    So, there are as many different ways to distribute in this case, as many there are different subsets \r\n" );
document.write( "    in the set of 5 elements.\r\n" );
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document.write( "    The answer to the last question is well known: there are  = 32 different subsets of the set \r\n" );
document.write( "    of 5 distinguishable objects.\r\n" );
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document.write( "    So, the answer to the case 1 is   = 32 ways.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now, cases when the person B or C receives nothing are absolutely symmetric to Case 1.\r
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\n" ); document.write( "\n" ); document.write( "So, the answer to the problem's question is $\"3%2A2%5E5\"$ = 3*32 = 96.
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