Prove $\left(\dbinom nk \right)= \left(\dbinom{k+1}{n-1}\right)$

Question

I need to prove $\left(\!\dbinom nk \!\right)= \left(\!\dbinom{k+1}{n-1}\!\right)$ where the double parens denote multiset coefficients and $n,k$ are integers with $1 ≤ k≤ n$ using an algebraic proof.

I have already tried, but it doesn't work out.

Answer 1

$$\left( \dbinom nk \right) =\binom{n+k-1}k =\binom{n+k-1}{(n+k-1)-k} =\binom{(k+1)+(n-1)-1}{n-1} = \left(\dbinom{k+1}{n-1}\right)$$