[{"title":"movie 2",categories:["Comedy","Romance","Family","Coming of Age"]},{"title":"movie 3",categories:["Action"]},{"title":"movie 1",categories:["Comedy","Horror","Romance","Family"]},]

db.collection.aggregate([{"$addFields":{"categoryCount":{$size:{$setIntersection:[["Comedy","Horror","Romance"],"$categories"]}}}},{"$match":{categoryCount:{$gt:0}}},{"$sort":{categoryCount:-1}},{"$project":{categoryCount:0}}])