Calculate the number of different ways to place $k$ identical balls into $n$ urns, assuming:

1. that there is at most one ball in each urn;
2. that the number of balls possible in an urn is unlimited.
1. We just apply the definition: $c^{\prime}$ is $\binom{n}{k}$.
2. A bit more difficult... It is $\binom{k+n-1}{n-1}$.

Solution to exercise $12 \mathrm{Si}$ if we temporarily number the faces of the cube, there are $6!=720$ possibilities. But several configurations correspond to the same cube! There are 24 configurations (count them), so finally 30 different cubes.