Question

There are nine different positions on a baseball team. If a team has 17 players how many different line-ups can the team make? (Assume every player can play every position.) The team can make different line-ups. Baseball games consist of nine innings. A team wants to change its line-up every inning. If no game goes to extra innings, and a season consists of 147 games, how many complete seasons can the team play without repeating a line-up? The team can play complete seasons without repeating a line-up. (Your answer should be an integer.)

Answer 1

Answer:

A) 24310

B) 18 seasons

Step-by-step explanation:

A) We are given the team has 17 players and there are 9 different positions in the team.

This is a combination question and thus, the number of different line-ups the team can make is;

C(17, 9) = 24310

B) We are told the basketball games consists of 9 innings.

Thus,

Number of games you can fill = 24310/9 = 2701.1111

And then we are told a season consists of 147 games.

Thus;

Number of complete seasons can the team play without repeating a line-up =

2701.1111/147 ≈ 18 seasons