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 How many ways are there to put 5 balls in 3 boxes if the balls are distinguishable but the boxes are not?

 

I think this is it: 

 

so we have 

5 balls (distinguishable)

 

3 boxes (undistinguishable)

 

5 0 0 → 1 way

4 1 0 → 5 ways

3 2 0 → 10 ways

3 1 1 → 10 ways

2 2 1 → 10 ways

 

total = 36 ways... but i don't think this is right. is this right? thanks!

 Mar 10, 2021
 #1
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I get the same answer, so I think you're right!

 Mar 10, 2021
 #2
avatar+721 
+2

(OP speaking here) Noooo!!! I thought I was right, but I was wrong. I don't even know what the answer is anymore :(

 Mar 10, 2021
 #3
avatar+144 
0

2 2 1 is 15 ways not 10.

Total 41

 Mar 11, 2021

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