If there are ...
20 materials for tails, 30 materials for bodies, 20 materials for thoraxes, 10 materials for hackles and 15 materials for wings (and I always used all of them, and didn't even create ribs), I could tie 1,800,000 diferent flies and put one on the board every day for 4,931.5 years without repeating.
But I would have trouble thinking of all those names.
I don't look at the fly tying section much anymore.
Tough to imagine being so limited...
Using the same materials in different ways can produce wildly different styles.
And you forgot the hundreds of hook options... Tubes, shanks, and articulation techniques should not be overlooked while looking at the frame of your flies...
And beads versus barbells versus sculpin heads...
And even Double Akroyds...
Or you could end up with 95 variations of 1 fly! I suspect though this is one time when statistics are not lying! They are telling us nothing, so can't be lying.
Another way to look at it is this. We live in an infinate universe, but we know not everyone ties flies. Therefore, the average population of fly tiers is a finite number devided by infinity. Which is zero. If the average population of fly tiers is zero then the actual population is also zero. Which means that any flies you see on here are the product of a deranged imagination.