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

sherwyo Aug 15, 2021

#1**0 **

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.

Guest Aug 15, 2021

#3**0 **

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