4 baseball players each stand at different corners of

M7MBA wrote:4 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?

A. 4
B. 6
C. 16
D. 24
E. 256

The sentence “Two arrangements of baseball players are considered different only when the relative positions of the players differ.” means that the arrangement ABCD is the same as BCDA, which in turn is the same as CDAB etc. So, let’s keep the player A fixed at the home plate and find the number of ways we can arrange players B, C and D on the three bases. We see that we can do this in 3! = 6 ways. Thus, there are 6 ways we can arrange the players around the diamond.

Alternate Solution:

This is a circular permutations problem, since the baseball diamond can be likened to a circular table with 4 players being seated. We thus use the formula (n - 1)!, where n is the number of players. Thus, we have:

(n - 1)! = (4 - 1)! = 3! = 6

Answer: B