mongodb distinct() in an array
I believe the best way to achieve that is by using the aggregation framework:

db.collection.aggregate(
    {$unwind : "$ccNameCount"},
    {$match : {
                "ccNameCount.ccName" : "ATCC"
    }},
    {$group: {
        _id : "$ccNameCount.paperCount"
    }},
    {$group: {
        _id : "count",
        total : {"$sum" : 1}
    }}
);


This will give you the distinct count of paperCount for ccName="ATCC" in the results total field.

Also, If you need to know each of the distinct values besides the total count you can use the $addToSet operator:

db.collection.aggregate(
    {$unwind : "$ccNameCount"},
    {$match : {
                "ccNameCount.ccName" : "ATCC"
    }},
    {$group: {
        _id : "$ccNameCount.paperCount"
    }},
    {$group: {
        _id : "count",
        total : {"$sum" : 1},
        distinctValues : {$addToSet : "$_id"}
    }}
);