Answer
$720$
Work Step by Step
If we want to choose $k$ elements out of $n$ regarding the order, not allowing repetition, we can do this in $_{n}P_k=\frac{n!}{(n-k)!}$ ways.
The order matters here, thus we have to use permutations. We have $10$ samples for $3$ spots, thus $_{10}P_{3}=\frac{10!}{(10-3)!}=10\cdot9\cdot8=720$
