A gymnastics competition has 4 gymnasts. How many different top-3 rankings are possible?

To solve this problem, we can 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 4 gymnasts (n=4) and we want to find out the number of ways to rank the top 3 (r=3).

So, we can plug these values into our formula:

P(4, 3) = 4! / (4-3)!

Calculating the factorials:

4! = 4 * 3 * 2 * 1 = 24 (4-3)! = 1! = 1

So, P(4, 3) = 24 / 1 = 24

Therefore, there are 24 different top-3 rankings possible in the gymnastics competition.