Counting Customers That Are In Multiple Groups

I have a large table that tells me customers and mailings (~4 million rows). So for each customer, I see what mailing(s) they received. It is at the mailing level so if a customer received 2 mailings, their will be 2 records for that customer number, one for each mailing they received. There are 3 different mailings.I am trying to calculate the count of customers that received all 3, as well as those that received 1&2 only, 1&3 only, and 2&3 only. For example:

CustNo Mailing
Tim 1
Tim 3
Dan 1
Dan 3
Jane 1
Max 1
Max 2
Max 3
Lauren 2
Lauren 3

Results:

All 3 - 1
1&2 only - 0
1&3 only - 2
2&3 only - 1

I have tried doing some funky table joining and EXISTS, but the query runs and runs because of how much data it has to sift through. Here is the code I am using to find Mailing 1&2 only customers, but I am not even sure it is getting me the right numbers. There are 2 different types of customers as well which is why I have custtype in there.

Code:
select a.custtype,count(distinct a.custno)
from myTable a
inner join (select distinct custno from mytable where [mailing]=2) b
on a.custno=b.custno
where a.[mailing]=1
and not exists(select * from myTable c where a.custno=c.custno and c.[mailing]=3)
group by a.custtype