Permutation question: Pick out 2 items from 4 items which 2 duplicated, is there any formula? If given ABBC, find the permutations if 2 letters are picked.
If I calculate manually, they are:
AB, AC, BA, BB, BC, CA, CB, 7 permutations.
Is there any formula to solve this type of question?
(Meaning, picking r number of letters from n number of letters with duplicated letters)
Suppose you had $n$ unique letters ${X_k}$, and letter $X_k$ were present in $r_k$ copies.

Then the number of unique pairs of letters, can be computed as $n (n-1) + \sum_{k} \mathrm{sgn} (r_k-1)$.

The term $n(n-1)$ count the number of pairs where letters are distinct, and remaining sum counts same letter pairs.
Permutation of n things taken r at a time out of which k are repeated is 

$\frac{n!}{(n-r)!k!}$

In your question , n=4 r=2, k=2

so total permutations is  $\frac{4!}{2!2!}$=6