Math experts? Help?

Hello.  Long story short, I'm working on the demographics of the various dragon species in my D&D campaign setting.  But I'm struggling with some of the necessary math.  
Say I know the number of breeding females of a particular species.  And I know how many clutches of eggs should be hatching each year on average.  All females are equally likely to be incubating a clutch at a given time, and clutches (conveniently) take exactly one year to hatch.  (For one example, there are 271 breeding females, and an average of 1.105187136 clutches hatching per year.)  
How do I calculate the probability of there being one clutch of eggs at a given time?  Or two clutches, or three?  (Etc.)

If I undertand correctly all females give birth al the same time of the year.

So it would be:

Number of females * probability of incubating a clutch

If clutches are equally distributed along the year then it would be

(Number of females * probability of incubating a clutch) / 12

Id they are not (meaning the probability is different each month/week...) it would be:

(Number of females * probability of incubating a clutch) * Probability of that period

I don't know if that is what you're asking but I hope this helps you

Thank you, I think that'll help me get un-stuck.