Question: there are 49 student in the room. the teacher claimed that there are at least 5 of them have their brithday in the same month. is it true ? why?
Suppose there is a maximum of 4 students with their birthday in the same month.
Since there are 12 months in a year, then you could have a class with 48 (12*4) students with 4 students having a common birthday in each different month.
But if there is a 49th student, then that student's birthday must fall in a month already occupied by 4 other students, making at least 5 students with a birthday in the same month.