You don't supply any table data so it isn't clear where the output came from But... I give it a try.
You mention you want distinct records so first about that. It is important to know that distinct is actually a simplified "group by". With this in mind you can easily group the records in the way you like.
SELECT eventid, ofparticipants, EventName, EventDate
WHERE EventDate IN (date1, date2, ...)
GROUP BY eventid, EventDate;
Keep in mind that by using eventid first in the group by, you only will get one record with that eventid. But if eventid is the primary index of this table you can leave it out because it will always be a distinct value.
Hopefully this will get you going and otherwise you might add some extra info (like some table records and the output you expect)