There are 10 students participating in a spelling bee. In how many ways can the students who go first and second be chosen?

The order matters.[tex]k [/tex] objects can be chosen out of [tex] n [/tex] objects, when the order matters, in [tex] P(n,k)=\dfrac{n!}{(n-k)!} [/tex] ways.So, the answer is [tex] P(10,2)=\dfrac{10!}{8!}=9\cdot10=90 [/tex] ways.