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Mathematics 25 Online
OpenStudy (anonymous):

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 139 games, how many complete seasons can the team play without repeating a line-up?

OpenStudy (wolf1728):

A baseball team consists of nine players. However, a team usually consists of a number much larger than this. So is it going to be a line-up chosen from 9 players each inning for 139 games?

OpenStudy (anonymous):

Sorry, the line up is 17.

OpenStudy (wolf1728):

Okay, so each inning, a line-up is chosen from 17 players. How many players are chosen each time? Also, does the order matter? In other words is 1, 2, 3 a different line-up from 1, 3, 2 ?

OpenStudy (anonymous):

16677181699666569 different line ups. If you can't repeat them, I'd imagine the order would matter, but the problem doesn't say.

OpenStudy (wolf1728):

I'd say for each line-up you would be choosing nine players from 17. This equals 17! / (9! * 8!) = 24,310 and if we rotate those 24,310 combinations in all possible ways (9!) then we have 24,310 * 362,880 = 8,821,612,800 ways. That's more than enough for one season. However, it is still a small number compared to your answer of 16,677,181,699,666,600 Well, that;s it for me. Hope it helps.

OpenStudy (anonymous):

Sorry it took so long to respond...really, I posted part B of the question, because I had gotten part A (The 16,677...). Sorry I didn't see the connection and for the confusion. Thanks anyways.

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