Im not entire sure how to explain this, but I know what a factorial is and how to use it in a basic sense. I guess you can say the number of variations of abcd is 4*3*2*1=24, right?

How would I figure out something like this mathematically:

the number of ways you can use capital and lowercase a's

aa AA aA Aa

theres only two variations, a and A. 2*1=2.

so my logic clearly doesnt work here lol

Also, how would I figure out something like how many variations are possible with a dataset of 3 members, with the dataset being populated with the possible genders being born

example:

b-b-b

g-g-g

b-g-g

b-g-b

etc

Im sure I didnt explain this well, and im not even sure if this is the forum it goes to but I would really like an answer to this, because trying to figure out how many variations that can occur the long tedious way is well.... tedious

thank you for any help