The reason for choosing option (1) "Dear Sir/Dear Madam, Yours faithfully" when you don't know the recipient's name in a formal letter is as follows:

1. Addressing the Recipient: "Dear Sir/Dear Madam" is a polite and common way to address someone when you don't know their name. It is gender-neutral and suitable for formal communication.

2. Closing the Letter:  "Yours faithfully" is a traditional and formal way to close a letter when you don't know the recipient's name. It conveys respect and professionalism. This closing is typically used in formal business correspondence.

Options (2), (3), and (4) do not follow the conventions of formal letter writing. They either use overly informal language or inappropriate closings for a formal context, which could be considered disrespectful or unprofessional in formal communication.