Show that if eight people are in a room, at least two of them have birthdays that occur on the same day of the week.

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The Pigeonhole Principle: If $n + 1$ objects are placed into $n$ boxes, then some box contains at least 2 objects.

There are $n=7$ days(‘boxes’), but we have $n+1 = 8$ people (‘objects’). Therefore at least two of eight people have birthdays that occur on the same day of the week.

Show that if eight people are in a room, at least two of them have birthdays that occur on the same day of the week.

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Question ID: mtid-5-stid-8-sqid-2623-qpid-1093