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# Baseball team consists of 20 players, 5 of whom are pitchers

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Intern
Joined: 04 Feb 2004
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Baseball team consists of 20 players, 5 of whom are pitchers [#permalink]  23 Apr 2005, 17:49
Baseball team consists of 20 players, 5 of whom are pitchers and 15 position players. If the batting order consists of 8 differnet position players and 1 pticher, and if the pitcher is always last in the order, then how many different batting orders are there for this baseball team?
Manager
Joined: 22 Apr 2005
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We are picking ordered combinations of 8 from 15.
It is 8P15 = 15!/(15-8)!
For each ordered combination we are independetly picking one out of 5 pitchers.

X = 5 * 15! / 7!
VP
Joined: 13 Jun 2004
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Agree with Tyr

my "old-school" method : (15*14*13*12*11*10*9*8)*5
which is the same than 15!*5/7!
Manager
Joined: 15 Feb 2005
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Re: COmbination 2 [#permalink]  26 Apr 2005, 07:40
rc1979 wrote:
Baseball team consists of 20 players, 5 of whom are pitchers and 15 position players. If the batting order consists of 8 differnet position players and 1 pticher, and if the pitcher is always last in the order, then how many different batting orders are there for this baseball team?

Just to clarify incase the question was how many different teams can be selected then we would use 15C8 instead of 15P8 right?
Re: COmbination 2   [#permalink] 26 Apr 2005, 07:40
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