Question for Nathan re: Thief of Baghdad

thief_q.txt

How many unique permutations are there for a sequence of size n with n_i number of elements of type e_i?

E.g. 

The sequence [a a b b] has 4 elements with n_1 = 2; n_2 = 2; and elements e_1 = a and e_2 = b.

The unique permutations of this sequence are:

1: a a b b
2: a b a b
3: a b b a
4: b a b a
5: b b a a
6: b a a b

Update: OK, so it turns out to me (n_1 + n_2)! / (n_1 ! * n_2 !)