I need to find the probability of 320 or more flaws in a 10km length of fibre optic cable. There is an average of 1.5 flaws per 50m.

I could solve this using:

P(X≥320) = 1 - [P(X=0) + P(X=1) + ... + P(X=319)]

But this would be extremely long and tedious to do, plus it wouldn't be an appropriate method.

Is there any other way I could get to my answer in a appropriate method?

(post links if necessary)