Maya help

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Fastest way to do it is using a mesh boolean. Depending on your mesh and the placement of the boolean-mesh, the result can be quite messy though and will need some cleanup. (Like eliminating n-gons by connecting vertices with edges for example. Mayas "triangulate mesh" function can help you a bit with that, but it's sometimes quite messy itself, so....)
First thing you do is, you create a cylinder in the size of your drain. Place it so that it intersects with your sink at the right place. Make sure it goes all the way through! Then, select your sink first, then SHIFT-select the cylinder and go to Mesh>Booleans>Difference. The result should look kinda like this:

Spoiler below!

As you can see, the boolean created quite a lot of ngons which will require fixing, but both sphere and drain stayed perfectly in shape, which would have been difficult to achieve by hand. On the other hand, the resulting geometry is not very useful for high-poly modeling, because you can't smooth a topology like that very well, due to a lack of proper edgeloops...there are pros and cons to almost every technique!