If the picking or arranging different things at different positions required we use combination. But in this question no need of that. So you can use permutation in this case.
$$P^8_3= \frac {8!}{5!}$$
And other way as mentioned by one user in comment.
To pick president we have 8 options. Then for vice-president we have 7 options left. For treasurer we have 6 options. Then we have,
$$8 \times 7 \times 6$$