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Combinations Problem

  • Thread starter temaire
  • Start date
  • #1
279
0

Homework Statement


There are three girls and six boys on the school softball team. The team consists of a pitcher, a catcher, four infielders, and three outfielders. How many ways can the nine different positions be filled if the pitcher must be a girl and the catcher must be a boy?


Homework Equations


[tex]_n{C}_r=\frac{n!}{(n-r)!r!}[/tex]


The Attempt at a Solution


The answer to this problem is [tex](_3{C}_1)(_6{C}_1)(7!)[/tex]. However, can someone explain the 7! part?
 

Answers and Replies

  • #2
737
0
The 7! refers to how many ways you can assign the 7 remaining people to the infield and outfield positions after assigning a girl and a boy to be pitcher and catcher.
 
  • #3
279
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This is what I had thought. However, there are two positions not one, that the rest are assigned to. Doesn't that affect the answer?
 
  • #4
737
0
I'm assuming each of the infield and outfield positions are considered different (e.g. left field, right field, center field...)
 
  • #5
279
0
Thanks Ted, that's exactly what I was looking for. :cool:
 

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