$Match, $OR, $group

Hello guys, if you can help me I need help with a query.
I have a document called Response with 3 fields, here an example:
[
  {
    "userId": "1",
    "questionId": "1",
    "answerIndex": 1
  },
  {
    "userId": "1",
    "questionId": "2",
    "answerIndex": 0
  },
  {
    "userId": "2",
    "questionId": "1",
    "answerIndex": 1
  }

I need to count how much users replied question 1 with answer 1 and question 2 with answer 0.
I tried to write this query:

db.responses.count( { $and: [ { $and : [ { questionId: { $eq: "1" } }, { answerIndex: { $eq: 1 } } ] }, { $and : [ { questionId: { $eq: "2" } }, { answerIndex: { $eq: 0 } } ] } )

but it's not working because I don't know how to isolate the user.

I'd be very grateful if anyone can help me, thanks!
I think I have to use $group on userId but I don't know exactly how


db.collection.aggregate([
  {
    "$match": {
      $or: [
        {
          questionId: 1,
          answerIndex: 1
        },
        {
          questionId: 2,
          answerIndex: 0
        }
      ]
    }
  },
  {
    $group: {
      _id: {
        userId: "$userId"
      },
      count: {
        $sum: 1
      }
    }
  }
])