$\begin{aligned} & \text { [Combinations and Permutations]} \\ & {[\text { Problems with Constraints }]}\end{aligned}$

There are 12 books on a shelf. In how many ways can five books be chosen from them such that no two of them are next to each other?
By putting the remaining books in correspondence with white balls, and the removed ones with black balls, we obtain a particular case of problem $\underline{60403}$.

## Answer

$\mathrm{C}_{8}^{5}=56$ ways.