Ghafoura Iqbal
Answered question
2022-07-18
Answer & Explanation
Nick Camelot
Skilled2023-06-10Added 164 answers
To understand why among any group of 367 people, there must be at least two with the same birthday, we can analyze the problem using the Pigeonhole Principle.
The Pigeonhole Principle states that if there are more pigeons than there are pigeonholes, then at least one pigeonhole must contain more than one pigeon. In this scenario, the pigeons represent the people in the group, and the pigeonholes represent the possible birthdays.
In this case, there are 367 people in the group, and only 366 possible birthdays (assuming we are not considering leap years). This means that there are more people (pigeons) than there are possible birthdays (pigeonholes).
According to the Pigeonhole Principle, since there are more people than there are possible birthdays, there must be at least two people with the same birthday. This is because if each person has a distinct birthday, we would need at least 367 possible birthdays to accommodate all the people, which is not the case.
Therefore, among any group of 367 people, there must be at least two people with the same birthday.
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