題組內容

7. (15%) There are N students in a class. How large N will let the probability of at least two students having the same birthday exceed 90%? Note: A year has 365 days.
【Hint: You may use the following characters:

(3) \( m \times (m + 1) \times (m + 2) \ldots (m + k) \leq \left(m + \frac{k}{2}\right)^{k + 1} \)