Count the number of pairs in Pandas DataFrame

Question

I have a dataframe like this:

df = pd.DataFrame(
    columns=['a', 'b'],
    data={
        'a' : [1, 1, 1, 2, 2, 2, 3, 3, 3],
        'b' : [1, 2, 2, 1, 2, 3, 4, 4, 4]
    }
)

How can I add a column named c containing number of same pairs of a and b in df:

c = [1, 2, 2, 1, 1, 1, 3, 3, 3]

Pair a=1 b=1 is present 1 time, a=1 b=2 two times, a=2 b=1 one time, a=3 b=4 three times and so on.