SOLUTION: in how many ways 5 different objects can be distributed among 3 persons so that exactly one person receives no object

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Question 1140056: in how many ways 5 different objects can be distributed among 3 persons so that exactly one person receives no object
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
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Let the three persons be  A,  B  and  C.

Case 1.  The person  A  receives nothing. 

    Then the person B receives some subset of 5 different objects, and the person C receives the rest 
    (receives the complement to the set that B receives).


    So, there are as many different ways to distribute in this case, as many there are different subsets 
    in the set of 5 elements.


    The answer to the last question is well known: there are 2%5E5 = 32 different subsets of the set 
    of 5 distinguishable objects.


    So, the answer to the case 1 is  2%5E5 = 32 ways.

Now,  cases when the person  B  or  C  receives nothing are absolutely symmetric to Case 1.

So,  the answer to the problem's question is  3%2A2%5E5 = 3*32 = 96.

Solved.