Counting entries in SQL which meet a selective criteria

I have a tables which stores the type of account users create for a product. There are 3 possible paths.

1. They can either create a trial account, then create a full account.
2. They can create a full account only.
3. They can create trial account oly.

In the first case, 2 entries would be created, while the other cases would create 1 entry. example source table below:

+------+--------------+
| user | account_type |
+------+--------------+
| 1    | trial        |
+------+--------------+
| 1    | full         |
+------+--------------+
| 2    | full         |
+------+--------------+
| 3    | full         |
+------+--------------+
| 4    | trial        |
+------+--------------+
| 4    | full         |
+------+--------------+
| 5    | trial        |
+------+--------------+
| 5    | full         |
+------+--------------+
| 6    | trial        |
+------+--------------+
| 7    | full         |
+------+--------------+

I would like to calculate the number of users who created a trial account followed by a full account, as well as those who went straight to create a full one. envisioned final table below:

+-------------------+------------------------+
| full_account_only | trial_and_full_account |
+-------------------+------------------------+
| 124               | 256                    |
+-------------------+------------------------+

My query so far is :

select sum(case
             when account_type_cnt = 1 then
              1
           end) as "full_account_only",
       sum(case
             when account_type_cnt = 2 then
              1
           end) as "trial_and_full_account "
  from (select user, count(distinct(account_type)) as account_type_cnt
          from tbl
         group by user)

but I realize it will not fulfill the criteria of counting users who only made a full account. Can somebody kindly help solve this?

Answer

You can use two levels of aggregation. I would put the counts in separate rows, like this:

select num_trial, num_full, count(*) as num_users
from (select user,
             sum(case when account_type = 'trial' then 1 else 0 end) as num_trial,
             sum(case when account_type = 'full' then 1 else 0 end) as num_full
      from t
      group by user
     ) u
group by num_trial, num_full;

You can easily modify this to put the values in columns instead:

select sum(case when num_trial > 0 and num_full = 0 then 1 else 0 end) as only_trial,
       sum(case when num_full > 0 and num_trial = 0 then 1 else 0 end) as only_full,
       sum(case when num_full > 0 and num_trial > 0 then 1 else 0 end) as both
from (select user,
             sum(case when account_type = 'trial' then 1 else 0 end) as num_trial,
             sum(case when account_type = 'full' then 1 else 0 end) as num_full
      from t
      group by user
     ) u
group by num_trial, num_full;