Question

Nine students ask to visit a college admissions counselor. Each scheduled visit includes one student. In how many ways can they be scheduled??

Answer 1

When you have to count in how many ways you can arrange something, you need permutations: you have 9 possible students to schedule as first, the second visit will be scheduled with one of the remaining 8 students, the third one with one of the remaining 7 students, and so on until the last one, therefore:

9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362880

The students can be scheduled in 362880 ways.

Answer 2

There are $n!$ ways to order $n$ objects.

So, the answer is $9!=362,880$ ways.