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counting and probability intermediate

Problem

There are people in a room. what is the largest value of such that the statement "At least people in this room have birthdays falling in the same month" is always true?
(A)
(B)
(C)
(D)
Solution
Pretend you have people you want to place in boxes, because there are months in a year. By the Pigeonhole Principle, one box must have at least people
Final answer
D