There are nine different positions on a baseball team. If a team has 17 players

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? 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 94 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.

Explanation / Answer

No. of ways of filling 1st position is 17, 2nd position is 16, 3rd position is 15 .... 9th position is 9

Therefore total no. of different line ups possible:

17*16*15*14*13*12*11*10*9 =
8,821,612,800 different lineups

Total no. of innings per season:
94*9 = 846

No of complete seasons team can play without repeating a line up:

8,821,612,800 / 846 = 10,427,438 seasons.

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