In Major League Baseball, There Are Five Teams In The West

In Major League Baseball There Are Five Teams In The Western Division

In Major League Baseball there are five teams in the Western Division of the National League: Arizona, Los Angeles, San Francisco, San Diego, and Colorado. How many different orders of finish are there for these five teams? Place your answer in the blank. Do not use any decimal places or commas. For example, 45 would be a legitimate entry.

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The question posed pertains to determining the number of possible permutations for the finishing order of five teams within the Western Division of Major League Baseball's National League. To address this, it is essential to understand the concept of permutations, which refer to the arrangements of a set of items where the order of those items matters.

In this scenario, we are dealing with five distinct teams: Arizona, Los Angeles, San Francisco, San Diego, and Colorado. Since each team must occupy a unique position in the final standings, the problem reduces to calculating the number of ways to permute five items. Mathematically, the total number of arrangements of n distinct objects is given by n factorial, denoted as n!, which is the product of all positive integers up to n.

Applying this to our problem, the total permutations for five teams are calculated as 5!, which equals 5 × 4 × 3 × 2 × 1. Performing this calculation yields:

  • 5 × 4 = 20
  • 20 × 3 = 60
  • 60 × 2 = 120
  • 120 × 1 = 120

Therefore, the total number of different possible finishing orders for these five teams is 120. This figure encompasses all possible permutations, from one team finishing first and the others following in every conceivable sequence, to the reverse order.

Understanding permutations is important in sports analytics, especially when evaluating potential standings or predicting final league positions based on various scenarios. In sum, the total number of distinct finish orders for the five teams in the Western Division is 120.

References

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