determining how many products are in how many categories

# product table (simplified):
create table p (  id char(22) not null primary key,  name text,  desc text
);

# product category table (simpl.):
create table pc (  id char(22) not null primary key,  name text,  desc text
);

# table that maps products into categories:
create table p_pc (  id char(22) not null primary key,  pid char(22) not null references p(id),  pcid char(22) not null
referencespc(id)
 
);
create index i_ppc_pid on p_pc(pid);
create index i_ppc_pcid on p_pc(pcid);
create unique index i_ppc_pid_pcid on p_pc(pid, pcid);

There are about 50k rows in p, 40k in pc, and 140k in p_pc. Most 
products are only placed in 1 category, some in 2, fewer in 3, and fewer 
stills in 4, 5, 6 categories.

I want to know how many products are placed in 1 category, how many in 
2, and so on. Here's my query:

select count(pid),num_cat from (  select pid,count(cid) as num_cat  from ppc group by pid) as f
group by num_cat;

A sample output (4000 products are categorized in 5 different places, 
4998 in 4, and so on):
 count | num_cat
-------+---------  4000 |       5  4998 |       4  7502 |       3 10001 |       2 17499 |       1
(5 rows)

However, this query is taking about 2.5 minutes. Any idea on how to make 
it faster?

-- 
dave