+283
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.
+6251 I'm seeing 28
\(\dbinom{6+3-1}{3-1} = \dbinom{8}{2} = 28\)
\(\left( \begin{array}{ccc} 6 & 0 & 0 \\ 5 & 1 & 0 \\ 5 & 0 & 1 \\ 4 & 2 & 0 \\ 4 & 1 & 1 \\ 4 & 0 & 2 \\ 3 & 3 & 0 \\ 3 & 2 & 1 \\ 3 & 1 & 2 \\ 3 & 0 & 3 \\ 2 & 4 & 0 \\ 2 & 3 & 1 \\ 2 & 2 & 2 \\ 2 & 1 & 3 \\ 2 & 0 & 4 \\ 1 & 5 & 0 \\ 1 & 4 & 1 \\ 1 & 3 & 2 \\ 1 & 2 & 3 \\ 1 & 1 & 4 \\ 1 & 0 & 5 \\ 0 & 6 & 0 \\ 0 & 5 & 1 \\ 0 & 4 & 2 \\ 0 & 3 & 3 \\ 0 & 2 & 4 \\ 0 & 1 & 5 \\ 0 & 0 & 6 \\ \end{array} \right)\)
