[{"name":"Some name","products":[{"product_name":"a"},{"product_name":"b"},{"product_name":"c"}]},{"name":"Some name","products":[{"product_name":"c"},{"product_name":"b"},{"product_name":"a"}]},{"name":"Some name","products":[{"product_name":"a"},{"product_name":"b"}]}]

db.collection.update({"name":"Some name","products.product_name":{$not:{$all:["a","b","c"]}}},{"$set":{"products":[{"product_name":"b"},{"product_name":"c"},{"product_name":"a"}]}})