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SQL count distinct question

Tags: count, distinct, sql, having
When I try to do this, I get an invalid syntax near ',' error.  Is this not possible? I am just trying to get a count of how many insurance claims each individual member(memid) has for each provider(provid) on each day(startdate).  I use this in the HAVING clause of a larger query because I want to only show people who have over a certain number of these instances.  

This doesn't work:
SELECT count(DISTINCT memid, startdate, provid)
FROM claim;

This does work and displays all of the lines, but I just want the count of those lines, not the actual info:
SELECT DISTINCT memid, startdate, provid
FROM claim;
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Question Stats
Zone: Microsoft
Question Asked By: lorenkii
Solution Provided By: amit_g
Participating Experts: 5
Solution Grade: A
Views: 169
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