14. Combination with repetition: Selecting $k$ elements from $n$ different elements in an unordered but repeatable manner is called a $k$-combination with repetition of $n$ elements. Try to calculate the number of $k$-combinations with repetition of $n$ elements.
14. Given $n$ elements numbered $1,2, \cdots, n$, take $k$ combinations with repetition $a_{1} a_{2} \cdots$ $a_{k}$. Since repetition is allowed, set $a_{1} \leqslant a_{2} \leqslant \cdots \leqslant a_{k}$,
define $f:\left(a_{1}, a_{2}, \cdots, a_{k}\right) \rightarrow\left(a_{1}, a_{2}+1, \cdots, a_{k}+k-1\right)$,
it maps each $k$-combination with repetition of $n$ elements to a $k$-combination without repetition of $n+k-1$ elements, and vice versa, $f$ is a one-to-one mapping, hence the number of $k$-combinations with repetition of $n$ elements is $\mathrm{C}_{n+k-1}^{k}$.