: Among any group of 367 people, there
Nari yaragani
Answered question
2022-07-23
: Among any group of 367 people, there must be at least two with the same birthday, because
there are only 366 possible birthdays.
Answer & Explanation
xleb123
Skilled2023-06-03Added 181 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 you have more pigeons than pigeonholes, at least one pigeonhole must contain more than one pigeon.
In this context, the 366 possible birthdays represent the pigeonholes, and the 367 people represent the pigeons. Since there are more people than there are possible birthdays, by the Pigeonhole Principle, at least two people must have the same birthday.
We can express this mathematically as follows:
Let's assume the opposite, that is, assume that no two people in the group of 367 share the same birthday. Since there are only 366 possible birthdays, each person would have a unique birthday. However, this contradicts the fact that we have 367 people in the group. Therefore, our assumption is false, and there must be at least two people with the same birthday.
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