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Homework Help: Combinations Problem

  1. May 19, 2008 #1
    1. The problem statement, all variables and given/known data
    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?


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


    3. 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?
     
  2. jcsd
  3. May 19, 2008 #2
    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.
     
  4. May 19, 2008 #3
    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?
     
  5. May 19, 2008 #4
    I'm assuming each of the infield and outfield positions are considered different (e.g. left field, right field, center field...)
     
  6. May 20, 2008 #5
    Thanks Ted, that's exactly what I was looking for. :cool:
     
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