Chapter 13, Problem 16RE

Baseball In how many ways can 2 teams from 14 teams in the American League be chosen without regard to which team is at home?

To determine

To find: In how many ways can 2 teams from 14 teams in the American League be chosen without regard to which team is at home?

Answer to Problem 16RE

91 ways.

Explanation of Solution

Given:

2 teams from 14 teams in the American League be chosen without regard to which team is at home.

Formula used:

$C\left(n, r\right) = \frac{n!}{r!\left(n - r\right)!}$

Calculation:

we need to choose 2 teams in the American League.

Here order is not significant hence this is a case of combination.

Number of ways 2 teams can be chosen from the American League is given by $C\left(14, 2\right)$.

$C\left(14, 2\right) = \frac{14!}{2!\left(14 - 2\right)!} = \frac{14!}{2!12!}$

$= 14*\frac{13}{2} = 13*7$

$= 91$

There are 91 ways 2 teams can be chosen from the American League.