how many ways can I cut a stick of length n doing m cuts

Question

How many ways can I cut a stick of length $n$ doing $m$ cuts? $1 < m < n$

For example: with a stick of length 4, I can cut it in the following ways using 2 cuts:

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Answer 1

It's basic stars and bars. Very quickly: you have $n-1$ possible cutting points, out of which you have to pick $m$. So, it's

$${n-1} \choose m$$

Answer 2

You have $m$ cuts to place on a stick. I guess the cuts are indistinguishable, so there will be $n-1$ possible places where you can cut the stick, thus the total number of options will be $${{n-1}\choose{m}} = \frac{(n-1)!}{(n-1-m)! \cdot m!}$$.