#### Answer

$132,860$ ways

#### Work Step by Step

The birthday of the first person can be any day from the $365$ days.
Since the birthdays should be different, the second person's birthday can only be a day from the remaining $364$ days (Birthday of first person is excluded from the options that second person can have).
Using multiplication principle, we have
Number of ways = $365\times364 = 132,860$.