The question follows a Poisson Distribution, where the average number of people booking a trip (λ) is 7 , 3 and 2 if they are north american, european or another nationality respectivelly.
And what I have to do is to say what is the probability of out of 10 chosen people, 4 not being either european or north american.
And here's what I tried to do: used the Poisson formula with λ=2 and x=4 (representing the 4 people that can't be european or north american) and then I used the Poisson formula again but now using λ=12 and x=6 ( representing the other 6 people that can be any nationality) and then did the sum of both. But I couldn't reach the right answer.
I'm not sure what I'm missing, or if I'm going with a wrong approach.
Hint: The conditional distribution of the number of "other," given that $10$ people booked, is binomial, $n=10$, $p=\frac{2}{7+3+2}$.