Answer :
The largest value of n such that the statement "at least n people in this room have birthdays falling in the same month" is always true is 5
How to determine the value
From the given information, we have 52 people in the room
Note that there are 12 months in a year
Let's divide the number by people by the months of the year
⇒ [tex]\frac{52}{12}[/tex]
⇒ 4 remaining 4
If 48 people are evenly distributed over twelve months, then there will be four people born in each month.
The remaining four people can be placed each in any of the twelve different months.
Hence, if 52 people are evenly distributed as possible, there will be eight months with four people and four months with five people.
Thus, the largest value of n such that the statement "at least n people in this room have birthdays falling in the same month" is always true is 5
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