Chapter 6.8, Problem 9E

i.

To determine

To find the number of different teams matchups.

Answer to Problem 9E

There are $225$ different team matchups which could be there in the finals.

Explanation of Solution

Given:

There are $15$ teams from Eastern Conference.

There are $15$ teams from Western Conference.

One team from each conference advances to the finals.

Formula Used:

If one event can occur in $m$ ways, and for each of these ways a second event can occur in $n$ ways, then the number of ways that the two events can occur together is $m\times n$ .

Calculation:

The different team matchups is:

  $=$ Teams fromEastern Conference $\times$ Teams fromWestern Conference

  $\begin{array}{l}=15\times 15\\ =225\end{array}$

Hence,

There are $225$ different team matchups which could be there in the finals.

ii.

To determine

To find the number of different matchups of the playoff teams.

Answer to Problem 9E

There are $64$ different matchups of playoff teams which could there be in the finals.

Explanation of Solution

Given:

There are $15$ teams from Eastern Conference of which $8$ teams make to the NBA playoffs.

There are $15$ teams from Western Conferenceof which $8$ teams make to the NBA playoffs.

One team from each conference advances to the finals.

Formula Used:

If one event can occur in $m$ ways, and for each of these ways a second event can occur in $n$ ways, then the number of ways that the two events can occur together is $m\times n$ .

Calculation:

The different matchups of playoff teams is:

  $=$ Playoff teams from Eastern Conference $\times$ Playoff teams from Western Conference

  $\begin{array}{l}=8\times 8\\ =64\end{array}$

Hence,

There are $64$ different matchups of playoff teams which could there be in the finals.

iii.

To determine

To answer and explain the statement.

Answer to Problem 9E

No.

The probability that two teams in the NBA playoffs meet in the finals cannot be determined.

Part b only considers possible matchups. The probability of two teams reaching the finals is not random, but depends at least partially on how good the teams are.

Explanation of Solution

Given:

There are $15$ teams from Eastern Conference of which $8$ teams make to the NBA playoffs.

There are $15$ teams from Western Conference of which $8$ teams make to the NBA playoffs.

One team from each conference advances to the finals.

No.

The probability that two teams in the NBA playoffs meet in the finals cannot be determined.

Part b only considers possible matchups. The probability of two teams reaching the finals is not random, but depends atleast partially on how good the teams are.