Poisson and binomial distributions

I composed this question: A hospital has 20 ambulances and on average 2 break down a day. There are five ambulances in reserve and if more then five ambulances break down in a day there are problems. What is the probability that in a 30 day period there will be problems? My approach is this: I use a Poisson distribution to calculate the probability of more than five ambulances breaking down in a day (I get 0.0166). Now I use a binomial distribution (with p=0.0166) to calculate the probability that in 30 days (30 trials) there will be more than 0 days with problems. I get 0.3948. Is my approach correct?