Time Capsule/Airport Express/Ethernet question

You will need an ethernet switch to distribute to all the ethernet ports in your rooms.

 

A switch won't be what you need. You'll need a router at the laundry room to distribute IP addresses to all of the Ethernet ports.

Is your modem also a router or is it strictly a modem? If it's the former you can just use the Extreme and Express in bridge mode to have them act as wireless access points. If it's the latter you will need to either use the Extreme as a router between your modem and the Ethernet ports in your Laundry room, or use a wired router in its stead and again set up the Extreme and Express as wireless access points.

 

I think you need to be a little more specific.

Are you using a router now? getting internet? Or is that ethernet cabling just that, cabling only? By "modem" are you referring to something your ISP gave you? Like a cable modem?

Do the ethernet cables all enter a box of some sort already? Or are they just separate cables?

Even if you use cable, you need a router. If you already have one, that could be it. If it's already routing and sending to the different rooms via ethernet, and all you're trying to do is attach the AE and TC to use as wireless access points, then they probably can be configured in bridge mode, and probably you want a roaming wifi network (one big one instead of separate ones; description on how to set it up should be in the documentation with the TC, or check on Apple's site. If this is the case no need for a switch or other router.