select count(anything_star_included_but_not_the_nullable_column_name) from the_table;

grant select on HumanResources.Department to TestUser;
go

deny select on HumanResources.Department (ModifiedDate) to TestUser;
go

-- then 

exec ('select count(DepartmentID) RecordCount
    from HumanResources.Department') as user = 'TestUser';

-- runs just fine, returning 16 as RecordCount, but either 

exec ('select count(1) RecordCount 
    from HumanResources.Department') as user = 'TestUser';

-- or

exec ('select count(*) RecordCount 
    from HumanResources.Department') as user = 'TestUser';