At a spelling bee, there are 5 students competing. How many top-2 rankings are possible?

To solve this problem, we need to use the concept of permutations. A permutation is an arrangement of objects in a specific order. The order of arrangement of the object is very important. The number of permutations of n objects taken r at a time is given by:

P(n, r) = n! / (n-r)!

where n! denotes the factorial of n.

In this case, we have 5 students (n=5) and we want to find the number of ways to choose the top 2 (r=2).

Step 1: Calculate n! = 5! = 54321 = 120

Step 2: Calculate (n-r)! = (5-2)! = 3! = 321 = 6

Step 3: Substitute these values into the formula to get P(5, 2) = 120 / 6 = 20

So, there are 20 possible top-2 rankings for the 5 students.