An insurance company supposes that the number of accidents that each of its policyholders will have in a year is Poisson distributed, with the mean of the Poisson depending on the policyholder. If the Poisson mean of a randomly chosen policyholder has a gamma distribution with density function g(λ) = λe−λ, λ  0 what is the probability that a randomly chosen policyholder has exactly n accidents next year?