Counting Distinct Values Of A Column Group By Another Column

I have this table ("people") and an example of possible rows:

id(key) COL 1 COL2 department country name
1 xx yy KPP USA John
2 zz kk KPP USA John
3 ss ff TLL USA John
4 ww qq PPO Italy Marco
5 jj uu PPO Italy Marco

I have to count the number of distinct DEPARTMENT for each NAME; so, for John should be 2 (KPP and TLL) and for Marco 1 (PPO).

I have tryed in this way:

SELECT
COUNT(DISTINCT department) AS NumberOfDifferentDepartments
FROM people
GROUP BY name;

But Access says me there is a syntax error.

I'm working with MS Access 2002.