Ways of arranging $k$ cards in a deck of $N$ cards I have a deck of $N$ cards numbered $1, \ldots N$. I want to count the number of ways that $k$ cards may appear in order. For example, if $k = 3$, I want to count the number of ways that of having a deck such that card $1$ appears before card $2$ appears before card $3$. The remaining $N - 3$ cards can be arranged arbitrarily. Note: card $1$ must appear before card $2$, but there can be $\geq 0$ cards inbetween them.
I am struggling to start on this question - I thought perhaps I could apply stars and bars, but I wasn't sure how to guarantee the ordering.

(Answer from comments)
There is $1$ way to arrange $k$ cards in any specific order (ascending, in this case).
There are $\binom{N}{k}$ ways to position those $k$ cards within a deck of $N$ cards.
Finally, there are $(N-k)!$ ways to arrange the remaining cards.
The total is therefore:
$$\binom N k \cdot (N -k)!=\frac{N!}{k!}$$
