I require your help in my research project.

Problem 1:

We are filtering a suspension of 1ml containing 1250 cells, through a micro-filter containing 1500 wells with pores. This is 80% filter saturation.

If filtration were random, on avarage how manny wells would contain no cells? how manny would contain 1 cell? how manny would contain 2 cells? and 3? and more than 3?

How would this be distributed with 50% filter saturation (750 cells per ml)?

Problem 2:

If we have a 1ml of a suspension containing 1250 cells and a random distribution. How big is the chance that somewhere in that solution an boxed area exists where 2 cells are within a vollume of 1.4*10^6 square micrometers (1.4 nanoliters).

How big would this chance be for a suspension of 750 cells/ml

As i dont have much statistical background i cannot solve these problems, and i have no way of knowing the difficulty of these problems. Maby someone can solve them?

Good luck.