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? It is asking for a probability. The denominator is easy, I think it should be (n+p) choose m since we are looking for the number of ways to choose the m specified seats from all seats. I'm not sure what to write for the numerator, I was thinking n+p choose m since that will give the different ways that the red seats could be chosen, times (n+p)-m choose n-m which gives the choices that the non-red seats could be chosen. Any ideas would be very appreciated.