Baseball Batting OrdersDate: 10/14/2001 at 18:27:28 From: Erica Subject: Word problem! How many possible batting orders are there for a team of nine players? I have no clue how to even start figuring this out. Please help! Date: 10/15/2001 at 15:19:12 From: Doctor Ian Subject: Re: Word problem! Hi Erica, Often when a problem seems too big to tackle, you can make some progress by considering a smaller problem. Suppose there is only 1 player (a). Then there is only 1 possible order, right? a What if we add a second player (b)? He could go either before or after a, right? a -> ba ab So there are two possible orders for two players. What if we add a third player (c)? He could go in any position in any of the orders we already had: a -> ba -> cba bca bac ab -> cab acb abc So now we have 1*2*3 different orders. Let's try it for one more player (d): a -> ba -> cba -> dcba cdba cbda cbad bca -> dbca bdca bcda bcad bac -> [4 more orders] ab -> cab -> [4 more orders] acb -> [4 more orders] abc -> [4 more orders] Now we have 1*2*3*4 different orders. It looks as if when we add the n'th player, we multiply the number of possible orders by n (because there are n possible changes to each of the orders we had before). So if we keep going until we have 9 players, how many possible orders would we have? Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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