Problem to resolve these probabilities

I need to resolve the following problem:

There are 6 buckets and each bucket can hold a maximum of 16 balls. There are 48 balls that need to be located. Assuming that the balls can go everywhere with the same probability.

1.- How much is the probability to have an empty bucket?
2.- How much is the probability to have 2 empty buckets?
3.- Assuming that those 48 balls have to be located sequentially (in 3 consecutive buckets). Answer the questions 1 and 2.

Thanks in advance!!

Thanks Mark for your advice. I was trying for a couple of days before asking in the Forum but I was not very happy with my conclutions . I hope you could help me with it.

Initially I tried to answer the 1st question: "what is the probability that a bucket is empty?"

- All the balls have the same probability: Prob.to have a ball anywhere?pr(1 ball)=48/96=0.5
- Probability to have an empty bucket:

Prob.of empty bucket?pr(EmptyBucket)
Prob.of having any ball in the bucketbucket?pr(BusyBucket)

pr(EmptyBucket)=1-pr(BusyBucket)
pr(BusyBucket)=pr(1ball)+ pr(2ball)+..+ pr(16ball)=0.5+?0.5?^2+?+?0.5?^16
pr(BusyBucket)=(0.5-?0.5?^17)/(1-0.5)=0.99
pr(EmptyBucket)=1.525??10?^(-5)

I think my calculations are not right because I have not taken into consideration that I only have 48 balls. The problem is that I am not sure how to take that into account during the calculations. How should I do to consider in the calculations that those 48 balls need to be allocated between all those 96 possible places (in the 6 available buckets)?

Thanks again!