- #1
indigojoker
- 246
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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?
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?