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Chapter 6: Q4RE (page 440)

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

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

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01

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.

02

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=mn

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 .

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Most popular questions from this chapter

How many subsets with more than two elements does a set with 100elements have?

In how many different ways can five elements be selected in order from a set with five elements when repetition is allowed?

a) State the generalized pigeonhole principle.

b) Explain how the generalized pigeonhole principle can be used to show that among any 91 integers, there are at least ten that end with the same digit.

Prove the identity\(\left( {\begin{array}{*{20}{l}}n\\r\end{array}} \right)\left( {\begin{array}{*{20}{l}}r\\k\end{array}} \right) = \left( {\begin{array}{*{20}{l}}n\\k\end{array}} \right)\left( {\begin{array}{*{20}{l}}{n - k}\\{r - k}\end{array}} \right)\), whenever\(n\),\(r\), and\(k\)are nonnegative integers with\(r \le n\)and\(k{\rm{ }} \le {\rm{ }}r\),

a) using a combinatorial argument.

b) using an argument based on the formula for the number of \(r\)-combinations of a set with\(n\)elements.

Suppose that bis an integer with b≥7. Use the binomial theorem and the appropriate row of Pascal's triangle to find the base- bexpansion of (11)b4[that is, the fourth power of the number (11)bin base-bnotation].
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