Prove that at least two people in Atlanta Georgia have the s

Prove that at least two people in Atlanta, Georgia, have the same initials, assuming no one has more than four initials. What is the probability that 3 random people will have the same birthday (month and day, assuming 365 days in a year)?

Solution

There are 26 alphabets.

No of ways upto 4 initials can be there

(say alphabets can be repeated)

= 26+ 26²+26³+26⁴

= 475254

As both Atlanta, Georgia have more than 475254 population, definitely there should be repitition atleast for 2 individuals.