My suspicion is that there are not really that many throws. I suspect a whole lot of them are not so different, but are variations on a smaller number of common throws.
Your leg may do exactly the same move, but since your hands contact points can be difference, this make different throws and require different set up.
Let's use hip throw for example. Your arm can:
1. wrap around your opponent's waist.
2. under hook his shoulder.
3. over hook his shoulder.
4. lock his head.
5. push behind his head.
6. lift his back belt.
7. wrap his arm.
8. push up under his chin while his back touch your back.
This already make 8 different hip throws.
There are 62 different categories of throw (only 11 categories are shown below) such as:
1. 35 different foot sweep.
2. 32 different leg block.
3. 15 different single leg.
4. 12 different horizontal foot scoop.
5. 9 different upward foot scoop.
6. 9 different leg spring.
7. 9 different shoulder throw.
8. 8 different hip throw.
9. 7 different front cut.
10. 7 different inner hook.
11. 4 different knife hook.
12. ...
My friend told me that someone in China wrote a book of "81 different ways to do single leg". I still have not found that book yet. But I can come up at least 15 different ways to do "single leg".