Question

There are nine different positions on a baseball team. If a team has 18 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 86 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

9 positions

18 players

total number of different line-ups can be found out by using combination

number of lineups =

number of lineups =

number of lineups = ​​​​​​​​​​​​​​

number of lineups = 48620

nine innings.

A team wants to change its line-up every inning​​​​​​​​​​​

season consists of 86 games

so in a season number of innings = number of innings in a game * number of games in a season

number of innings in a season = 9 * 86 = 774

to find number of seasons without repeating a lineup, divide number of lineups by number of innings per season

Team can play, without repeating a line-up = 48620/774 = 62.82

So, The team can play ​​​​​​​62 complete seasons without repeating a line-up.