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N people sit down at random a classroom containing n+p seats

  1. Jan 23, 2009 #1
    n people sit down at random a classroom containing n+p seats. There are m red seats (m<=n) in the classroom, what is the probability that all red seats will be occupied?

    I know the bottom should be n+p choose n but I'm not sure what the numerator should be, any ideas would be great.

    I was thinking n+p choose m since that will give the different ways that the red seats could be chosen, times n+p choose n-m which gives the choices that the non-red seats could be chosen.

    Or: [tex] \frac{ C^{n+p} _{m} C^{n+p} _{n-m} } { C^{n+p} _{n} } [/tex]

    Does this logic make sense?
     
  2. jcsd
  3. Jan 23, 2009 #2
    Re: probability

    Close, but after having allocated m people amongst the n+p seats there are now only n+p-m seats to allocate the remaining n-m people.
     
  4. Jan 23, 2009 #3
    Re: probability

    then:
    [tex]
    \frac{ C^{n+p} _{m} C^{n+p-m} _{n-m} } { C^{n+p} _{n} } [/tex]?
     
  5. Jan 24, 2009 #4
    Re: probability

    EDIT: my error; see the other post.
     
    Last edited: Jan 24, 2009
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