Richard Nixon actually said...

The random selection method shall use 365 days to represent the birthdays (month and day only) of all registrants who, prior to January 1, 1971, shall have attained their nineteenth but not their twentieth year of age.

Context

Proclamation 3989—Random Selection of Military Service for Registrants Who Attain the Age of Nineteen During the Current Year

06/15/1970

https://www.presidency.ucsb.edu...

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