the probability that out of 10 person all born in June at least two have the same birthday. Explain nicely in notebook pls

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{June} \mathrm{has} 30 \mathrm{days}. \\ \mathrm{Now} \\ \mathrm{Probability} \mathrm{that} \mathrm{atleast} \mathrm{two} \mathrm{have} \mathrm{same} \mathrm{birthday} \\ =1-\mathrm{No} \mathrm{two} \mathrm{have} \mathrm{same} \mathrm{birthday} \\ \mathrm{Now} \mathrm{first} \mathrm{person} \mathrm{has} \mathrm{birthday} \mathrm{on} \mathrm{some} \mathrm{day}, \mathrm{then} \mathrm{second} \mathrm{have} 29 \mathrm{options} \\ \mathrm{so} \mathrm{that} \mathrm{his} \mathrm{birthday} \mathrm{does} \mathrm{not} \mathrm{clash} \mathrm{with} \mathrm{first} \mathrm{person}, \mathrm{similarly} \mathrm{third} \\ \mathrm{person} \mathrm{will} \mathrm{have} 28 \mathrm{options} \mathrm{so} \mathrm{that} \mathrm{his} \mathrm{birthday} \mathrm{does} \mathrm{not} \mathrm{clash} \mathrm{with} \\ \mathrm{first} \mathrm{and} \mathrm{second} \mathrm{person} \mathrm{and} \mathrm{so} \mathrm{on}.... \\ \mathrm{Hence} \\ \mathrm{Required} \mathrm{Probability}=1-1\times \frac{29}{30} \times \frac{28}{30}\times \frac{27}{30}\times \frac{26}{30}\times \frac{25}{30}\times \frac{24}{30}\times \frac{23}{30}\times \frac{22}{30}\times \frac{21}{30} \\ =1-\frac{29\times 28\times 27\times 26\times 25\times 24\times 23\times 22\times 21}{{30}^9} \end{gathered}$$

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards