Points:
1. For sending the email, Ramesh, Mahesh and Suresh would have to open separate TCP connections to the mail server in all cases under SMTP protocol.
2.For receiving the emails, Sonali, Pooja and Vidhi would have to open 3 separate TCP connections with their mail server in all cases under POP/IMAP protocol.
3. SMTP uses persistent TCP connections.
Worst Case:
All three persons send the email at different times. At each time one TCP connection would be required between sender's mail server and recipient's mail server. So total 3 TCP connections in worst case.
Total no. of TCP connections required: 3(from client to mail server) + 3 (From sender's mail server to recipient mail server) + 3(from mail server to recipients) = 9 TCP connections
Best Case:
All three persons send the emails at the same time.SMTP uses persistent TCP connections. So one TCP connection will be opened between Sender's mail server and recipients' mail server and all three emails will be sent.
Total no. of TCP connections required: 3(from client to mail server) + 1 (From sender's mail server to recipient mail server) + 3(from mail server to recipients) = 7 TCP connections