I don't believe you can in MySQL 5.1.
You can work around it though - whatever the partition definition you can add the same as a condition to your count.
For example if it is a range partition on the ID column and p1 is ID < 10000, p2 ID < 20000 then
SELECT result, partition, count(ID)
FROM
(
SELECT result, ID,
case when ID < 10000 then p1
when ID < 20000 then p2
.....
end as partition
FROM
table
) s1
GROUP BY partition, result