Pregunta
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How many people must be in a room to be sure that at least two were born in the same month of the year? A. 2 people B. 12 people C. 3 people D. 13 people

Ask by Mcfarlane Perkins. in the United States
Mar 09,2025

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The answer is 13 people.

Solución

1. There are \(12\) months in a year, so there are \(12\) possible birth months. 2. By the pigeonhole principle, if we have more people than the number of months, then at least one month must have more than one person. 3. Therefore, with \(13\) people, at least one month must have at least two people born in it. 4. The correct answer is \(13\) people. Thus, the answer is D.

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Beyond the Answer

To ensure that at least two people share the same birth month, you only need 13 people in the room! This is because there are 12 months in a year. The "pigeonhole principle" states that if you have more items (people) than containers (months), at least one container must hold more than one item. Hence, with 13 people, at least two of them will definitely be born in the same month! This scenario is often a fun topic in probability and combinatorics. It highlights how seemingly simple questions can lead to intriguing mathematical principles. If you're curious about such principles, exploring more about the pigeonhole principle and its applications can really expand your understanding!

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