Combination

[fantasylo]

Dear all

I am looking at the number of combinations for this scenario.

I have the following options

a
b
c1/c2/c3 (choose 1)
d1/d2/d3 (choose 1)
e1/e2 (choose 1)

i) Maximum is 5 options
ii) If I choose d1, I cannot choose d2 or d3

Combinations of 5 (18 combinations)
a, b, c1, d1, e1
a, b, c1, d1, e2
a, b, c1, d2, e1
a, b, c1, d2, e2
a, b, c1, d3, e1
a, b, c1, d3, e2
a, b, c2, d1, e1
a, b, c2, d1, e2
a, b, c2, d2, e1
a, b, c2, d2, e2
a, b, c2, d3, e1
a, b, c2, d3, e2
a, b, c3, d1, e1
a, b, c3, d1, e2
a, b, c3, d2, e1
a, b, c3, d2, e2
a, b, c3, d3, e1
a, b, c3, d3, e2

Questions:
1) Is there a formula for this kind of scenario?

2) What is the number of combinations for combinations of 3?

Thank you for your assistance.