Laravel select random rows with distinct field

I have products table like this.

id        direction_id
______________________

1          1
2          2
3          2
4          2
5          1
6          3

I need to get one random product of all directions.

E.G.
Direction 1 - Product(1 or 5)
Direction 2 - Product(2 or 3 or 4)
Direction 3 - Product(6)

And i need to use Product model because I have a lot of relationships which i should use.

Thanks in advance!

via Chebli Mohamed