# Thread: Question about factorials (I think)

1. ## Question about factorials (I think)

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

2. You're right that this is not the right board, but then, I'm not sure either since one thread similar to this got moved from the simple probability and statistics board, and I do factorials, permutations and combinations in statistics.

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.
Here, there are repeats, and as such, is different. My way of solving this is this:

I first put two blanks: _ _

In the first blank, I can have either a or A, so, two possibilities.
In the second blank, I can get either a or A, so again two possibilities.

Total becomes 2 x 2 = 4

This works with more than two items too.

With abc, you can have:
aaa, aab, aba, aac, aca, abc, acb, abb, acc,
baa, bab, bba, bbb, bac, bca, bcc, bcb, bbc
caa, cab, cba, cbb, cac, cca, ccc, ccb, cbc

Which is obtained using the logic; 3 possibilities in each blank, hence, 3 x 3 x 3 = 27

IF there were no repeats, then 2! is the answer for the first case, and 3! for the second case.