Conditional to check if a certain category has posts

I am looking for a conditional statement that can test to see whether a certain pre-existing category has any posts in it.

Something along the lines of:

if (category 1, which already exists, has at least one post in it) {
such and such html here. Not a loop, but a piece of markup }

Since I’m making a braindead backend for a client the categories already have to exist so they can put posts in them.