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A math class has 25 students. Assuming that all of the students were born in the first
half of the year—between January 1st and June 30th— what is the probability that at
least two students have the same birthday? Assume that nobody was born on leap day,
so there are 181 possible birthdays.
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$\frac{_{24}^{181}\textrm{C}._{1}^{24}\textrm{C}+_{23}^{181}\textrm{C}._{2}^{23}\textrm{C}+_{22}^{181}\textrm{C}._{3}^{22}\textrm{C}+.................}{_{25}^{181}\textrm{C}}$