Stuck on this birthday problem

Question

Assume for simplicity that N people, all born in April (a month of 30 days), are collected in a room Consider the event of at least two people in the room being born on the same date of the month, even if in different years, e.g. 1980 and 1985. What is the smallest N so that the probability of this event exceeds 0.5?

Answer 1

It is very similar to this.

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7 persons are enough.

From the article linked above, we use the same strategy, and we get that $$\frac{30}{30} \times \frac{29}{30} \times \frac{28}{30} \times \frac{27}{30} \times \frac{26}{30} \times \frac{25}{30} \times \frac{24}{30}\le0.5$$ The answer follows.