EMAIL VIRUS

In $1999,$ a computer macro based on a popular suite of programs was launched through the

Internet. This macro came in the form of an email message that replicated itself via the first $50$

email addresses in a recipient's address list.

For example, person A sends the message to person B$,$ who inadvertently sends a copy of the

message to the first $50$ people in his email address book.

Assume that there are no duplicate recipients.

If the first email is called the first generation, how many emails in total will have been sent in

the first five generations?