Past SOA question

During a one-year period, the number of accidents per day was distributed as given below:



No. of Accidents ---------Days

0------------------------209

1------------------------111

2-------------------------33

3--------------------------7

4--------------------------3

5--------------------------2



the maximum likelihood estimates are lambda^=0.6 for the Poisson distribution and r^=2.9 and beta^=0.21 for the Negative Binomial distribution. Conduct the likelihood ratio test for choosing between the two models.



My question is, when I go to solve for the likelihood I don't know how to obtain p(1), p(2),... for the Neg. Binomial? That is, how do I solve

(2.9Choose1), (3.9Choose2), etc... to solve for the logliklihood? (Especially on an exam where I only have my calculator?)



Thanks

Past SOA question