SQL Query

Hi,

Following is the table Structure in DB:
id: auto increment integer
name: varchar(256)
person_id: an integer that references a person in a different table
type: two values - 0 or 1

0 means a person w/ type0
1 means a person w/ type1

Following values and (others not mentioned) are possible:
1 XXX 1 0
2 XXX 1 1
3 YYY 2 0
4 ZZZ 3 1
5 AAA 2 0

The following are what I like to find out - number of persons who
a) are just type 0
b) are just type 1
c) are both type 0 and type 1

Initially, I wrote a simple query to answer a)
select count(person_id) from TABLE where type = 0 AND person_id NOT IN (select person_id from TABLE where type = 1 group by person_id) group by person_id;

But, it is too slow to compute - almost ran for 10 hours and still not completed.
There is a index for each column - id, person_id, type

Please provide new SQL queries that is faster and does the above job.

Thanks!