Question

How can you find the number of possible outcomes of a playoff between two teams where the first team that wins four games wins the playoff?

Short answer

The number of possible outcomes of a playoff between two teams where the first team that wins four games wins the playoff is 70.

Step-by-step solution

Definition of Concept

Permutations: A permutation of a set is a loosely defined arrangement of its members into a sequence or linear order, or, if the set is already ordered, a rearrangement of its elements, in mathematics. The act of changing the linear order of an ordered set is also referred to as "permutation."

Lexicographic order: The lexicographic or lexicographical order (also known as lexical order or dictionary order) in mathematics is a generalization of the alphabetical order of dictionaries to sequences of ordered symbols or, more broadly, elements of a totally ordered set.

Find the total number of possible outcomes

Considering the given information:

Number of team =4

Using the following concept:

The number of possible playoff outcomes between teams where the first team to win n games wins the playoff$={\mathrm{m}}^{\mathrm{n}}$

Apply binary tree for the case when there are 4 win or 4 loose then World Series ends.

Therefore, the number of possible outcomes of a playoff between two teams where the first team that wins four games wins the playoff is 70 .