Astrology Probabilities

Excuse for my english. You can change whatever you like for this make more sense.

My mother is an astrologer, and I'm wonder about the different combinations of "aspects"
and positions in a natal chart.
People think that astrology isn't mathematical, or it's just guess.

I'm learning english, and one of my homework, is to explain something that I know.
So, I wish to know how many possibilities are there for each person to add to the work.

The components of a natal chart are:

1) 10 planets. They could be arranged OR NOT in any quantity of groups of any number. It
is not important the order inside the group. ABC = BCA.

Details: Let me tell that that is more complicated than that since there are frequency in
orbits of planets, so they group together every a specific amount of years, so a group (or
conjunction) of two of them could be possible just each 72 years, and adding one more to
the group could take hundreds of years.... Groups can happen being at almost or just the
same degree in the 360 wheel but there are different tolerances for each aspect... so let's
focuse just in the different possible groups.
Let's say that Is enough for me to know the total combinations if they could happen, rather
than the probabilities to happen this year or together.

2) Each planet or group of them could be in 4 different relations with others or in none.

Details: Each planet OR group of them could be spread over the wheel, making "aspects"
with other planets or group of them when they are at 120, 90, 180 or 60 degrees each
from other. When there is 120 degrees between them, is a trine. 90 for a cuadrature, 180
for an opposition, 60 for a sextile. Conjunction is also an aspect, but we are already
counting them as groups.

3) Each planet or goup, could be in one of 12 signs

(Signs are pies of 30 degrees. Just for you to know)

4) Each planet or goup, could be in one of 12 houses

(Houses are pies of approx. 30 degrees. Just for you to know)

Thanks.