Question 1129916: How many ways are there to place 4 distinct balls into 5 distinct boxes such that exactly 3 of the 5 boxes do not have any balls?
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How many ways are there to place 4 distinct balls into 5 distinct boxes such that exactly 3 of the 5 boxes do not have any balls?
# of ways to pick the two boxes to receive balls:: 5C2 = (5*4)/(1*2) = 10 ways
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# of ways to lace 4 distinct balls in those 2 distinct boxes::
(# in box A, # in Box B)
(0,4) 1 way
(1,3) 4 ways
(2,2) 6 ways
(3,1) 4 ways
(4,0) 1 way
Total (A,B) ways:: 16
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Final Answer:: 10*16 = 160
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Cheers,
Stan H.
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Answer by ikleyn(52780)  (Show Source):
You can put this solution on YOUR website! .
In this problem, the order of 2 selected boxes is important and does matter.
Therefore, we have 5*4 = 20 different box arrangements - not 10 combinations, as @stanbon uses.
Then the total number of ways is 20*16 = 320 - not 160.
The correct answer is 320 ways.
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