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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