+0

0
142
2
+183

How many ways are there to put 6 balls in 3 boxes if the balls are not distinguishable but the boxes are?

I got 7, but I wanted to check.

Oct 25, 2018

#1
+4402
+3

I'm seeing 28

$$\dbinom{6+3-1}{3-1} = \dbinom{8}{2} = 28$$

$$\left( \begin{array}{ccc} 6 & 0 & 0 \\ 5 & 1 & 0 \\ 5 & 0 & 1 \\ 4 & 2 & 0 \\ 4 & 1 & 1 \\ 4 & 0 & 2 \\ 3 & 3 & 0 \\ 3 & 2 & 1 \\ 3 & 1 & 2 \\ 3 & 0 & 3 \\ 2 & 4 & 0 \\ 2 & 3 & 1 \\ 2 & 2 & 2 \\ 2 & 1 & 3 \\ 2 & 0 & 4 \\ 1 & 5 & 0 \\ 1 & 4 & 1 \\ 1 & 3 & 2 \\ 1 & 2 & 3 \\ 1 & 1 & 4 \\ 1 & 0 & 5 \\ 0 & 6 & 0 \\ 0 & 5 & 1 \\ 0 & 4 & 2 \\ 0 & 3 & 3 \\ 0 & 2 & 4 \\ 0 & 1 & 5 \\ 0 & 0 & 6 \\ \end{array} \right)$$

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Oct 26, 2018
edited by Rom  Oct 26, 2018
#2
+183
+1

Thank You!

Oct 26, 2018