Important note, if you take a straw that separates into two split straws (kinda in a "Y" shape) that from a topological point of view is two holes, because one is for one of these paths, and the other is an extruded hole on the side of the first path. In topology you can't break or mend material, but you can pull, stretch, squeeze and move it all you want. So you can move one of the split straw "legs" to the bottom of the whole straw, getting a shape similar to a "V", it would look pretty much like a pair of pants. And topologically speaking it would be exactly the same. So... One straight hole for your mouth all the way down to your anus. Another two are there for your nostrils, that's 3 already. The rest are for your tear ducts, which have two holes on the edge of your eye, (so four in total) which merge and then connect to your nose.

So a human, from a topological perspective, is just a seven holed doughnut. Also Vsauce made a great video about that, with pretty great animations.

This fella explains it way better than I ever could..

https://youtube.com/watch?v=egEraZP9yXQ

Kissing with open mouths creates a hole from one butthole to another.

Nose is only one hole, topologically speaking. You can run a string from one nostril to the other.

One topological hole.

oh! but then why is it three holes and not nostril-to-mouth as a hole and other-nostril-to-butt as another hole, or some other combination

Nose is only one hole homie, runs from one nostril to the other. It takes the mouth to add a secondary orifilce. And it takes the anus to add a third orifice.

Topology for ya.