Franz Joseph's old blueprints break down the TOS Enterprise's security staff thusly:
Chief of Security (Lt. Cmdr.) ... 1
Security officers (Lt.) ... 5
Security Specialists (Ensign) ...84
From a total crew of 430.
If you're talking about the new Enterprise from the last movie, the "Experience the Enterprise" site said it had an overall crew of 1100, so I'm guessing more redshirts!