Find all documents where a particular field of all elements of a subcollection are inlcuded inside a given array in MongoDB / Mongoose

Working with MongoDB and Mongoose, let's say ,for example, that I have this schema:

var componentSchema = mongoose.Schema({
name             : String,
price            : Number
});

var partSchema = mongoose.Schema({
componentId        : { type: Schema.Types.ObjectId, ref: 'Component' },
quantity           : Number
});

var robotSchema = mongoose.Schema({
name             : String,
type             : Number,
parts            : [partSchema]
});

Every robot needs a set of components to be build.

Since a robot may need more than a single copy of a component (e.g. 10 bolts, 5 screws, 1 transistor...), we store inside the robot model an array of parts, where each part contain the reference to a component plus an additional field, quantity.

Now I'm interested in finding, given an array of component's names (or, eventually, given an array of componentIds) all the robots that I can build with those types of components (notice that a component doesn't include quantity, I just assume that I have an infinite amount of those component), ordered by the one that uses most components of the given array.

Robot A: 2 bolts, 2 transistors 
Robot B: 10 bolts, 2 capacitors, 3 bars of plutonium  
Robot C: 5 bolts, 1 capacitor, 5 transistors

I have [bolts, capacitors, transistors]. 
Query results:  

    Robot C  
    Robot A 

(In this order!)

Is it even possibile with a complex MongoDB query?