One-2-many relation - need distinct counts

Hi gurus,

I have table A, B and need a distinct count of
Accounts from A.  There is a one-2-many relation
between A and B.  Accounts # in A are all unique. 
However, in B there will be duplicates.  So the
problem I have is, when I join as follows:
Select Count(Distinct(account_no)) 
from A, B 
where A.Account_no = B.Account_no

I get the correct count.  If I do this:
Select Count(Distinct(account_no)), B.Account_type 
from A, B 
where A.Account_no = B.Account_no 
group by B.Account_type

I get wrong counts because there some are duplicated. 
I tried everything that I can think of - subquery, sub
table etc.  I would appreciate some help in writing
the query.  Thanks in advance.

PS

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