Choosing a Fan-out Strategy by Group Size

You are asked to design message delivery for three cases in the same product: a 1:1 DM, a 40-person work group, and a 2-million-subscriber public broadcast channel.

1. Describe the fan-out approach for each case and explain why a single strategy does not work for all three.
2. For the 2-million-subscriber channel, walk through exactly what happens server-side when a new message is posted.
3. Propose a hybrid optimization for the broadcast channel that improves perceived latency for actively-viewing members without reverting to full fan-out-on-write.