nested select within a DISCTINCT block

Hi, here i have a problem with this task...

I have a table "cancellation" which stores cancelled bookings and details of
charges etc
and a table "bookings" which stores details of bookings, for example:

cancellation(cancellation_id, booking_id, charge)
booking(booking_id, customer_id, product_package_id, details)

in the query, i wish to find, how many customers have booked for each
product_package_id. if there were 3 bookings for product_package_id=1, and
all these are cancelled and therefore exist in cancellation, then the query
result shoud display something like

package_id, #of bookings
1 0

here are what i tried

select distinct b.product_package_id,
count (distinct b.customer_id and not exists (select cc from cancellation cc
where cc.booking_id=b.booking_id)) from booking as b
group by b.product_package_id

and it doesnt work. the syntax within the DISTINCT is wrong, unsurprisingly.

i also tried
select distinct b.product_package_id,
count (distinct b.customer_id not in (select cc from cancellation cc where
cc.booking_id=b.booking_id)) from booking as b
group by b.product_package_id

it produced incorrect result. ie, for those canceled bookings are also
counted, producing
package_id, #of bookings
1 3

which supposed to be
package_id, #of bookings
1 0

could anyone give any hints please, many thanks !

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