Asked by Anonymous
                Kisha has five different marbles. How many different ways can she place the marbles into two bags so that at least one marble is in each bag?
            
            
        Answers
                    Answered by
            Reiny
            
    Assuming the 2 bags are distinguishable. 
then :
C(5,1)xC(4,4) + C(5,2)xC(3,3) + C(5,3)xC(2,2) + C(5,4)xC(1,1)
= 5 + 10 + 10 + 5
= 30
notice that this is row 1 5 10 10 5 1 of Pascal's triangle with out the leading and ending 1's.
If the 2 bags are indistinguishable, then there are half of the above, or 15
    
then :
C(5,1)xC(4,4) + C(5,2)xC(3,3) + C(5,3)xC(2,2) + C(5,4)xC(1,1)
= 5 + 10 + 10 + 5
= 30
notice that this is row 1 5 10 10 5 1 of Pascal's triangle with out the leading and ending 1's.
If the 2 bags are indistinguishable, then there are half of the above, or 15
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