[{"_id":null,"count":2,"students":[["a","b"],["a","c","d"],]}]

db.collection.aggregate([{"$unwind":"$students"},{"$group":{"_id":0,count:{$sum:1},"students":{"$push":"$students"},"initialStudent":{"$first":"$students"}}},{"$set":{"common":{"$reduce":{"input":"$students","initialValue":"$initialStudent","in":{"$setIntersection":["$$value","$$this"]}}},}},{$project:{"count":1,"students":["$common"]}}])