[{"_id":1,"name":"Project1","contributors":[{"_id":11,"name":"user1"},{"_id":22,"name":"user2"}]},{"_id":2,"name":"Project2","contributors":[{"_id":22,"name":"user3"},{"_id":44,"name":"user4"}]}]

db.collection.aggregate([{$match:{"_id":1}},{$unwind:"$contributors"},{$project:{contributor:"$contributors"}},{$match:{"contributor._id":22}},{$count:"projects"}])