14.1. In how many ways can $k$ items be selected from $n$ different items if the order in which the items are selected: a) matters; b) does not matter.
14.1. a) The first item can be chosen in $n$ ways, the second item in $n-1$ ways, $\ldots$, the $k$-th item in $n-k+1$ ways. In total, we get $n(n-1) \ldots(n-k+1)=\frac{n!}{(n-k)!}$ ways.

b) Each set of $k$ items, where the order of items is not considered, corresponds to $k!$ sets where the order of items is considered (this corresponds to choosing $k$ items from $k$ distinct items). In total, we get $\frac{1}{k!} \cdot \frac{n!}{(n-k)!}=C_{n}^{k}$ ways.