The 'chance' and 'design' group
These nouns are used to indicate whether something that happened was intended or not. Appointment, arrangement, and mistake are count nouns.
by accident by appointment by arrangement by chance by choice by coincidence by default by design by fluke by good fortune by happenstance by luck by mistake by necessity
It was only by chance that we found out there were three or four other people there.
Whether by design or accident his timing was perfect.
The boy had let off a fire extinguisher in the house by mistake.