Counting Question

Question: If I had X number of train cars and I wanted to know the probability of having Y or more people in a car when I have N total of people. How would I go about solving this?

I thought that this would be a good example of a SUM from k = Y -> N of combination(N k) ; however, my number does not seem to make sense. I have been stuck on this problem for a while now and I am not sure what the correct path is to solving it. Any and all advice would be helpful in understanding and solve this type of problem.

Thanks in advance!