Using a pandas DataFrame to get the count of the 10th most frequent value

I have a DataFrame that contains entries of place_ids such as:

place_id
11111
11111
22222
33333
44444
44444
...

I would like to get the count of the 10th most frequent value.

Here's what I've come up with:

print df.place_id.value_counts().nlargest(10).tail(1).values[0]

This seems like too much work. Is there an easier way to get the count of the 10th most frequent place_id?