There were 23 students running in a race. How many different arrangements of first, second, and third place are possible?

10626 different arrangements

Step-by-step explanation:

As we have a total of 23 students and we want to form groups of 3, where the order of the 3 students matters, we can solve this problem using a permutation of 23 choose 3.

The formula for a permutation of n choose p is:

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

So, using n = 23 and p = 3, we have:

P (23,3) = 23! / (23-3) ! = 23! / 20! = 23 * 22 * 21 = 10626

So we have a total of 10626 different arrangements of first, second and third place.