Helping people with computers... one answer at a time.
When an email message comes back to you because of a problem exactly who did or did not get the message depends on the error and where it happened.
I sent 4 recipients an e-mail. As it turns out, I got a notice from MAILER-DAEMON that the address not deliverable. I know it is because they changed their address, which I wasn't aware of. Should the other 3 recipients have received the e-mail? This situation occurs once in awhile, because people don't always tell quickly enough when they change addresses. So, my question in essence, like with tree lights, if one fails, do the others stay lit?
In your case it's fairly clear: the message probably was delivered to other three recipients.
In the general case, of course, things are never quite that simple.
On top of that things get more complicated because these days you're not even guaranteed to get a bounce back if something goes wrong.
I'll examine the possibilities.
Email makes several steps along its path from you to your recipients, and of course an error can happen at any point along that path.
Exactly what that implies to your delivery depends on:
Where along the way the error occurred.
The specific error that occurred.
The key in every case is to carefully read the error message for clues as to what broke, and where. I'm afraid I'll be saying that a lot in this article.
Let's look at a few examples.
Some errors are fairly obvious errors generated by your email program when you press the send button. Some programs will tell you that an email address is malformed, perhaps your account configuration is wrong, or perhaps your mail server is down.
In all these cases the mail never left your machine, and hence didn't make it to any of your recipients.
I have also seen email programs that generate their own "bounce" messages in this scenario. Rather than popping up an error message immediately (possibly because email isn't actually sent immediately, but rather queued to be sent in the background), on failure the email program manufactures a faux-bounce message and places it in your inbox.
The key is in the error message: it should have some indication of what the error was; in particular check the "From:" line - it'll probably be your own email program.
By "Your Mail Server" I mean, of course, your ISP's mail server which you've configured your email program to contact when sending mail - typically that's the "SMTP" server setting.
The most common cause of failure sending mail to your mail server is account validation. Either your account information is wrong (bad username or password, for example), your account configuration is wrong (bad mail server name, for example) or there's something else about the message that the server doesn't like (perhaps early spam detection, or size limits of some sort).
Regardless of whether that comes to you as an immediate popup message, or a bounce message, the information you care about is once again in the error message you receive.
Failures at this point also prevent all copies of the email from being sent - the message still hasn't left your machine.
Your mail server is then responsible for taking the single message you've sent, and sending it one at a time to each recipient. Errors at this point fall into two general buckets:
Your email server can't contact the recipient's email server
The recipient's email server refuses to take delivery of the message
In the first case you'll typically get an bounce from your email server telling you that it was unable to contact the remote server. Once again, read the text of the bounce message and you'll see something that says "unable to contact", the always helpful "bad or missing MX record" (the information that tells mail servers which mail server they should contact for someone's email address), or errors along those lines. The bounce message will come "From:" your mail server.
In the second case the bounce message may come either from your mail server, or from the recipient's mail server. In either case the reason will be included in the message. Common problems include:
the recipient's mail server's spam filter thinks your email is spam
the recipient's mailbox is full, or "over quota" and cannot accept any more mail until he or she cleans it out
the recipient's email account has been closed and no longer accepts mail
you've typed the recipient's email address in wrong
Regardless of the reason if the email has reached this point, then each failure is per-recipient - meaning that some of the emails will have made it, and others - the ones that result in an error message back to you - will not. The key here is that the error message will specifically reference one of the email addresses that you attempted to send to. It's that address that has the problem.
I absolutely get that the bounce messages can be confusing - there's often a lot of technical gobbledygook making the message difficult to understand.
Take the time to read it anyway.
Quite often the error will be buried within that mess - brush the mess aside and the reason for the failure may suddenly become quite clear.
Sometimes bounce messages are the equivalent of "It didn't work" - with no additional information as to why it didn't work.
When that happens the best you can do is to use the information in the "From:" line of that message to see which server along the sending path generated the error, and from that use the information above to make an educated guess as to what might have been wrong, and whether or not it's something you can fix.
And also, whether or not all, some or none of your recipients got the message.