Pandas dataframe fillna() only some columns in place

I am trying to fill none values in a Pandas dataframe with 0’s for only some subset of columns.

When I do:

import pandas as pd
df = pd.DataFrame(data={'a':[1,2,3,None],'b':[4,5,None,6],'c':[None,None,7,8]})
print df
df.fillna(value=0, inplace=True)
print df

The output:

     a    b    c
0  1.0  4.0  NaN
1  2.0  5.0  NaN
2  3.0  NaN  7.0
3  NaN  6.0  8.0
     a    b    c
0  1.0  4.0  0.0
1  2.0  5.0  0.0
2  3.0  0.0  7.0
3  0.0  6.0  8.0

It replaces every None with 0‘s. What I want to do is, only replace Nones in columns a and b, but not c.

What is the best way of doing this?