db={"fridges":[{_id:1,items:[{itemId:1,name:"beer"},{itemId:2,name:"chicken"}],brand:"Bosch",size:195,cooler:true,color:"grey",nbMax:2},{_id:2,items:[{itemId:1,name:"beer"},{itemId:2,name:"chicken"},{itemId:3,name:"lettuce"}],brand:"Electrolux",size:200,cooler:true,color:"white",nbMax:2},]}

db.fridges.aggregate([{$match:{$and:[{"brand":{$in:["Bosch","Electrolux"]}},{"color":{$in:["grey","white"]}}]}},{$project:{"itemsNumber":{$size:{"$filter":{"input":"$items","as":"item","cond":{$in:["$$item.name",["beer","lettuce"]]}}}},brand:1,cooler:1,color:1,nbMax:1}},{$match:{$expr:{$ne:["$nbMax","$itemsNumber"]}}}])