Solution

The total number of simple events is 

$(365)^n.$

The number of ways in which no one has birthday on same date is given by $P_n^{365}.$ Note that event $B= A^c.$

$$$$\begin{align*} P(A)&= \dfrac{\textrm{No. of simple events in A}}{\textrm{Total number of simple events}}\\ &= \dfrac{P_n^{365}}{(365)^n}\\\\ P(B)&= 1 - P(A)\\ &= 1- \dfrac{P_n^{365}}{(365)^n} \end{align*}

Answer