How do I calculate the number of unique permutations in a list with repeated elements? I know that I can get the number of permutations of items in a list without repetition using 

(n!)


How would I calculate the number of unique permutations when a given number of elements in n are repeated.

For example

ABCABD

I want the number of unique permutations of those 6 letters (using all 6 letters).
There is a specific formula for such problems:

Permute all elements, and remove permutations of elements that are identical, viz.

$\dfrac{6!}{2!2!}$
Do you want the number of combinations of a fixed size? Or all sizes up to 6? If your problem is not too big, you can compute the number of combinations of each size separately and then add them up. 

Also, do you care about order? For example, are AAB and ABA considered unique combinations? If these are not considered unique, consider trying stars-and-bars: How to use stars and bars (combinatorics)