How many people must be in a group to guarantee that 2 peopl

How many people must be in a group to guarantee that 2 people in the group have the same birthday (don’t forget leap year)?

Solution

Number of days in a leap year = 366 days

According to pigeon hole principle, if there are (n+1) pigeons and n holes, then there will be atleast 2 pigeons in same hole

Assuming number of days as holes, i.e. 366 holes, hence minimum pigeons required will be (366+1) = 367 pigeons

Hence there must be 367 people in a group to guarantee that 2 people in the group have the same birthday