Imagine we have the sentence
I am hungry, and luckily there happens to be a lot of apple trees nearby.
Should it be "happen to be" or "happens to be" in this instance? I believe the correct form is "happen to be" and that is because "a lot of apple trees" is plural. If the sentence was
I am hungry, and luckily there happens to be a big apple tree nearby.
I believe it would be correct, but I can't find any resources on the internet to check whether this assumption is true. Can anyone shed a bit of light on this? Thanks a lot!