# Combinatorics - divide objects into groups

How many different possibilities are there to divide $$n$$ different objects into 2 groups $$A$$ and $$B$$, if in group $$A$$ exactly $$n_a$$ objects in group $$B$$ exactly $$n_b$$ objects are to be assigned.

Since all n objects should be assigned to a group, $$n_a + n_b = n$$.

This is just $$\binom n{n_a}$$.
Choose the objects that go to $$A$$...the rest go to $$B$$ by default.