To determine the number of ways to choose students for first and second place from a group of 10 students, we need to consider that the order in which the students are chosen matters (since one will go first and the other second).
- Choose the first student: There are 10 possible choices since all students can be chosen at this point.
- Choose the second student: After the first student has been chosen, there are 9 remaining choices.
The total number of ways to choose the first and second student is given by:
\[ 10 \times 9 = 90 \]
Therefore, the answer is 90 ways.