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How many ways are there to put 4 balls in 3 boxes if the balls are distinguishable but the boxes are not?

 Aug 15, 2021
 #1
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The cases are {4,0,0}, {3,1,0}, {2,1,1}, {2,2,0}

 

Counting the number of ways in each case gives us an answer of 1 + 4 + 6 + 6 = 17.

 Aug 15, 2021
 #2
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The answer is 14

sherwyo  Aug 15, 2021
 #3
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sherwyo:

Thanks for telling the forum the answer but

next time how about saying thanks to your answer for their time and effort as well.

 

 

Guest answerer:

 

The reason you are out by 3 is your  2,2,0 case

 

You said 4C2 which was right but what is left behind is also a pile of 2. 

Once you have chosen one pile of 2 you have also chose its compliment.  So you have to divide by 2

6/2=3

That is why your answer was 3 too big.

Melody  Aug 16, 2021
edited by Melody  Aug 16, 2021

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