I have a dataframe like below :

data = {'RTG_ID': ['AA','AA','AA','BB','BB','CC','CC','CC','EE','EE','EE','GG','GG','FF','FF'], 'TYPE': ['CD','FF','EF','CD','EG','CD','EF','FF','CD','EF','HH','CD','EG','CD','TT']}
df = pd.DataFrame(data)

I like to get a count of the combinations based on type and RTG_ID. the order are not matter. it means combination A,B is same as B,A.

this is my desired output of dataframe :

output = {'RTG_ID': ['AA','AA','AA','BB','BB','CC','CC','CC','EE','EE','EE','GG','GG','FF','FF'],TYPE': ['CD','FF','EF','CD','EG','CD','EF','FF','CD','EF','HH','CD','EG','CD','TT'],'COMBINATIONS': ['CD,FF,EF','CD,FF,EF','CD,FF,EF','CD,EG','CD,EG','CD,FF,EF','CD,FF,EF','CD,FF,EF','CD,FF,HH','CD,FF,HH','CD,FF,HH','CD,EG','CD,EG','CD,TT','CD,TT'],'COUNT': [2,2,2,2,2,2,2,2,1,1,1,2,2,1,1]}
df_output = pd.DataFrame(output)

I have read How to count the combinations of unique values per group in pandas? but i like to have the combinations added into my orginal dataframe.