Savita and Hamida are friends. Find the probability that both of them have different birthday.

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Solution

Selecting $2$ days out of $365$ in $^{365} C_{2}$ ways.
Total choices $= 365 \times 365$
$\Rightarrow$ Probability $= \frac{^{365} C_{2}}{(365)^{2}} = \frac{365 \times 364}{2 \times (365)^{2}} = \frac{182}{365}$ .

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