$\text{ Each person can have birthday in }365\text{ ways. }$

$\text{ So n persons can have birthdays in }(365{)}^{\mathrm{n}}\text{ ways. }$

$\mathrm{A}=\mathrm{atleast} \mathrm{two} \mathrm{of} \mathrm{them} \mathrm{will} \mathrm{have} \mathrm{the} \mathrm{same} \mathrm{date} \mathrm{of} \mathrm{birth} \mathrm{of} \mathrm{a} \mathrm{non} \mathrm{leap} \mathrm{year} (\mathrm{Assuming} \mathrm{a} \mathrm{year} \mathrm{is} \mathrm{having} 365 \mathrm{days})$

$\text{ Number of ways in which all have different birthdays }={}^{365}\mathrm{P}_{\mathrm{n}}$

$\mathrm{P}\left(\mathrm{A}\right)=1-\mathrm{P}\left(\overline{\mathrm{A}}\right)=1-\frac{{}^{365}\mathrm{P}_{\mathrm{n}}}{(365{)}^{\mathrm{n}}}$