There are 27 students on the collage debate team. What is the probabil

Hi All,

This prompt is more a 'logic' problem than a math question. We have 27 students and 12 potential months in which those 27 students could possibly have their birthdays. It's possible that all 27 birthdays are in the same month or that the birthdays are "spread out" over the 12 months. We're asked for the probability that at least 3 of the birthdays are in the SAME month. Note that the prompt doesn't specify which month - so ANY month will do.

It might help to think in terms of how you might avoid having at least 3 birthdays in the same month. To do that, you would have no more than 2 birthdays per month. Over the course of 12 months, you could place (12)(2) = 24 of the birthdays and not have 3 or more in any given month. However, we have to place 27 birthdays - and if each of the 12 months already has 2 birthdays, then wherever you put those remaining 3 birthdays... there WILL be at least one month that includes at least 3 birthdays. Thus the probability of this outcome is 100% = 1.

Final Answer:

GMAT assassins aren't born, they're made,
Rich